A Coefficient Inside
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 45 of 64.
In |2x - 1| = 7, the expression inside the bars is 2x - 1. Split into two cases first. Each case is then a two-step equation: add 1 to both sides, then divide both sides by 2.
2x - 1 = 7
2x = 8
x = 4
or
2x - 1 = -7
2x = -6
x = -3
The two cases give x = 4 or x = -3. Check each answer in the original equation. For x = -3, the inside is 2 × (-3) - 1 = -7, and |-7| = 7, so the answer checks. Keep both answers.
Challenge
MediumSolve the equation |2x + 3| = 9 for x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Inequalities & Absolute Value
1What an Inequality Is
The Four SignsA Picture on a LineClosed or OpenReading It BackwardsRecap: What an Inequality Is4Two-Step Inequalities
Two StepsSubtract, Then FlipWith a FractionA Bracket on the WayRecap: Two-Step Inequalities2Adding and Subtracting
Add to Both SidesSubtract from Both SidesNegatives in the MixSolve, Then DrawRecap: Adding and Subtracting5Variables on Both Sides
x on Both SidesGather Toward the LargerBrackets FirstAlways True, Never TrueRecap: Variables on Both Sides11From Words to Inequalities
At Least, At MostMore ThanA Budget That ShrinksTwo LimitsRecap: From Words3Multiplying and Dividing
Divide by a PositiveMultiply by a PositiveThe FlipDividing by a NegativeNegative FractionsRecap: Multiply and Divide6Graphing Solutions
From Inequality to PictureIs the Endpoint In?A Flip on the LineRecap: Graphing Solutions9Absolute Value Equations
Distance from ZeroThe Equation |x| = 3Distance from a PointIsolate the Bars FirstA Coefficient InsideNo Solution, One SolutionRecap: Absolute Equations