Solve the following equations with absolute value. ( B ) 5 ∣ 6 x − 9 ∣ + 3 = 3 5\left|6x-9\right|+3=3

Welcome back. For this problem, we'd like to solve the equation five times the absolute value of six x minus nine plus three equals three. We know that the first step is going to be isolating that absolute value, so we need to start by trying to get the absolute value alone on the left side of the equation. The first thing we want to get rid of is this plus three, which we can do by subtracting three on both sides of the equation. That will cancel the plus three on the left, leaving us with five times the absolute value of six x minus nine, and on the right, we get three minus three, which is zero. Next, we have to get rid of this five, which is being multiplied by the absolute value, so we can get rid of it by dividing both sides of the equation by five. On the left side, the fives cancel, leaving us with the absolute value of six x minus nine, and on the right, we get zero divided by five, which is zero. Now we have an equation of the form absolute value equals zero, so this means that the thing inside the absolute value must be equal to zero. So that means that six x minus nine equals zero. Now we solve this equation. We can add nine to both sides of the equation to cancel this minus nine on the left, leaving us with six x is equal to zero plus nine, which is nine. Then, we divide both sides of the equation by six to cancel the coefficient of six on the left, leaving us with x equals nine sixths, which we can simplify to three halves. So we get the solution x equals three halves for our equation, which you can plug back into the original equation, and you will get a true statement. Great work.

Solve the following equations with absolute value. ( B ) 5 ∣ 6 x − 9 ∣ + 3 = 3 5\left|6x-9\right|+3=3

x = − 3 2 x=-\frac32 x = − 2 3

2. Linear Equations and Inequalities

Absolute Value Equations

Intermediate Algebra

2. Linear Equations and Inequalities

Absolute Value Equations

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Multiple Choice

Solve the following equations with absolute value.
(B) $5 ∣ 6 x - 9 ∣ + 3 = 3$

$x=-\frac32$

$x=0$

$x=\frac32$

$x=3$

Verified step by step guidance

Start with the given equation: \$5\left|6x - 9\right| + 3 = 3$.

Isolate the absolute value expression by subtracting 3 from both sides: \$5\left|6x - 9\right| = 3 - 3$.

Simplify the right side: \$5\left|6x - 9\right| = 0$.

Divide both sides by 5 to solve for the absolute value: $\left|6x - 9\right| = 0$.

Recall that $\left|A\right| = 0$ implies $A = 0$, so set the inside of the absolute value equal to zero: \$6x - 9 = 0$ and solve for $x$.

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Struggling with Intermediate Algebra?

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Solve the following equations with absolute value.
(B) $5 ∣ 6 x - 9 ∣ + 3 = 3$