https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-equations/v/absolute-value-equations 2022-11-16T04:22:43.7414897Z Intro to absolute value equations and graphs To solve absolute value equations, find x values that make the expression inside the absolute value positive or negative the constant. To graph absolute value functions, plot two lines for the positive and negative cases that meet at the expression's zero. The graph is v-shaped. Sal Khan video https://cdn.kastatic.org/googleusercontent/3Ux8GfhZeWAJQ5FTcCweUVMWJVCGMIjjAWVd2MDSBmrvMLgyLym3qrQ8uG3rT8glOqCOE00htgkezn4PZ-QQFVU Intro to absolute value equations and graphs To solve absolute value equations, find x values that make the expression inside the absolute value positive or negative the constant. To graph absolute value functions, plot two lines for the positive and negative cases that meet at the expression's zero. The graph is v-shaped. https://cdn.kastatic.org/ka-youtube-converted/u6zDpUL5RkU.mp4/u6zDpUL5RkU.mp4 641 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-equations/v/absolute-value-equations-1 2022-11-16T04:22:43.7414897Z Worked example: absolute value equations with one solution To solve absolute value problems with one solution, identify expression in absolute value bars. Recall absolute value is zero only if expression is zero. Make expression equal right-hand side. Use algebra to find x values that satisfy equation. Check solutions by plugging in. Graph solutions on number line. Mark points. Sal Khan video https://cdn.kastatic.org/googleusercontent/HDW2AzDlN8ANv_pCN05wzNbAOALOUuKlI60NG1WR2clTpSDOBLRv_TtPb72oJGNoVD2JrRHE5oiSvIr2HmCDxIgR Worked example: absolute value equations with one solution To solve absolute value problems with one solution, identify expression in absolute value bars. Recall absolute value is zero only if expression is zero. Make expression equal right-hand side. Use algebra to find x values that satisfy equation. Check solutions by plugging in. Graph solutions on number line. Mark points. https://cdn.kastatic.org/ka-youtube-converted/GwjiR2_7A7Y.mp4/GwjiR2_7A7Y.mp4 156 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-equations/v/absolute-value-equation-example 2020-06-23T07:22:42Z Worked example: absolute value equation with two solutions Solving the equation 8|x+7|+4 = -6|x+7|+6 which has two possible solutions. Sal Khan video https://cdn.kastatic.org/googleusercontent/iavpVH010pyRw3dq5tP_tvxV1KRFI91IACCqrc9PiYVdGTrbvu5QJUz62HPK69Ve2F2wjc74M66xs_WffXyrrOU Worked example: absolute value equation with two solutions Solving the equation 8|x+7|+4 = -6|x+7|+6 which has two possible solutions. https://cdn.kastatic.org/ka-youtube-converted/UvtWf4TVawE.mp4/UvtWf4TVawE.mp4 290 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-equations/v/absolute-value-equation-with-no-solution 2020-06-23T07:22:42Z Worked example: absolute value equations with no solution Solving the equation 4|x+10|+4 = 6|x+10|+10 to find that it has no possible solution. Sal Khan video https://cdn.kastatic.org/googleusercontent/-V8dP83T1WE5G_blxuU-FCfNFrm3FehEG2josNf-8ALbtglc5UKzaMKz5T-CYawH2M50-vC3gcYj1tFU8dCKHIQrbQ Worked example: absolute value equations with no solution Solving the equation 4|x+10|+4 = 6|x+10|+10 to find that it has no possible solution. https://cdn.kastatic.org/ka-youtube-converted/15s6B7K9paA.mp4/15s6B7K9paA.mp4 230 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-equations/e/absolute_value_equations 2021-06-30T16:39:16Z Solve absolute value equations Solve equations like 3|x+1| + 7 = 6|x+1| + 6. Sid Patel exercise https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-inequalities/v/absolute-value-inequalities 2022-11-16T04:22:43.7414897Z Intro to absolute value inequalities To solve inequalities with absolute values, use a number line to see how far the absolute value is from zero. Split into two cases: when it is positive or negative. Solve each case with algebra. The answer is both cases together, in intervals or words. Sal Khan video https://cdn.kastatic.org/googleusercontent/DC9HM-guQbuFnuwO8JtMaKMj72NgjLcfLaB8xp4jtfb4Wx-rp5CbU2x9AnS5bicfdJk1ngj7rGLwRmc2MmT9Gf0udw Intro to absolute value inequalities To solve inequalities with absolute values, use a number line to see how far the absolute value is from zero. Split into two cases: when it is positive or negative. Solve each case with algebra. The answer is both cases together, in intervals or words. https://cdn.kastatic.org/ka-youtube-converted/iI_2Piwn_og.mp4/iI_2Piwn_og.mp4 793 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-inequalities/v/absolute-value-inequalities-example-1 2020-06-23T07:22:43Z Solving absolute value inequalities 1 Sal solves the inequality |h|-19.5 < -12. Sal Khan video https://cdn.kastatic.org/googleusercontent/1M0nGgEl6_l-aQ3NZkMoZF6-kMQJPh4AJOzRg_vwxeP6Fj5zT67D7gYbrwn7mTcYxbssNYQ_iLTwepl3S0RrjjJX Solving absolute value inequalities 1 Sal solves the inequality |h|-19.5 < -12. https://cdn.kastatic.org/ka-youtube-converted/TvUCe6Bomy4.mp4/TvUCe6Bomy4.mp4 207 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-inequalities/v/absolute-value-inequalities-example-2 2020-06-23T07:22:43Z Solving absolute value inequalities 2 Sal solves the inequality |p-12|+4 < 14. Sal Khan video https://cdn.kastatic.org/googleusercontent/E2R2Es2XK0pRDZCqJaB6sJxa3raE7834QoqLspyzNKyFC-X8rbojhmginJn4Lk49meBJrsKVfQZju8KHqdL7RamV Solving absolute value inequalities 2 Sal solves the inequality |p-12|+4 < 14. https://cdn.kastatic.org/ka-youtube-converted/YKQLZOq4HTA.mp4/YKQLZOq4HTA.mp4 279 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-inequalities/v/absolute-inequalities-2 2020-06-23T07:22:41Z Solving absolute value inequalities: fractions Sal solves the inequality |2r-3 1/4| < 2 1/2. Sal Khan video https://cdn.kastatic.org/googleusercontent/Jjsgnn2cvZYX8uCOPZge1DUdv1b7d70YsmGYe2PtzalrItXS1HR1oEzewtAA8sTq4AcI8pLD7VIB57reYumrSvSd Solving absolute value inequalities: fractions Sal solves the inequality |2r-3 1/4| < 2 1/2. https://cdn.kastatic.org/ka-youtube-converted/x5EJG_rAtkY.mp4/x5EJG_rAtkY.mp4 450 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-inequalities/v/absolute-value-inequalities-example-3 2020-06-23T07:22:43Z Solving absolute value inequalities: no solution Sal solves the inequality |y|+22 ≤ 13.5 to find that it has no solution. Sal Khan video https://cdn.kastatic.org/googleusercontent/fCMCiUZX3ppAZH4RS4y9fq869TA1HTYvsQAyc8jR8SRI4NYT8wkKQ9tCrx1fGdJuckjtxpkw5udsbfSmg5pd_BAVJQ Solving absolute value inequalities: no solution Sal solves the inequality |y|+22 ≤ 13.5 to find that it has no solution. https://cdn.kastatic.org/ka-youtube-converted/y9MGpOGQVqQ.mp4/y9MGpOGQVqQ.mp4 155 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-inequalities/v/writing-and-using-inequalities 2020-06-23T07:22:43Z Absolute value inequalities word problem Sal solves a word problem about a carpenter by writing an appropriate absolute value inequality and solving it. Sal Khan video https://cdn.kastatic.org/googleusercontent/oKKoHjhn2AIxF1yQKWCowtstRAacOUQR8o9wfuk-NgdQxjvqVVPqcp5YpqEEvArJXuK5hHjKL9ETvEdyHoK76--Rlg Absolute value inequalities word problem Sal solves a word problem about a carpenter by writing an appropriate absolute value inequality and solving it. https://cdn.kastatic.org/ka-youtube-converted/RHe9X2HDEjA.mp4/RHe9X2HDEjA.mp4 278 Absolute value equations and inequalities https://www.khanacademy.org/math/algebra-1-eureka-squared-aligned/x15446f63b23e2a07:expressions-equations-and-inequalities-in-one-variable/x15446f63b23e2a07:solving-absolute-value-inequalities/e/solve-absolute-value-inequalities 2025-09-09T23:00:51.091323116Z Solve absolute value linear inequalities Solve absolute value inequalities algebraically and graphically. Nate Kinast exercise