QuestionSolve the equation $|3 x+5|=5 x+2$ . What are the possible values of $x$ ?

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, and is always non-negative. . The equation is $|3x+5|=5x+$ .
3. The absolute value of a quantity can be expressed as the quantity itself or the negative of the quantity.
4. We are looking for the value(s) of $x$ that satisfy the equation.

STEP 2

We can solve the equation by considering the two possible cases separately when $x+5$ is non-negative, and when $x+5$ is negative.
Case1 $x+5 \geq0$
In this case, the equation becomes $x+5=5x+2$ Case2 $x+5 <0$
In this case, the equation becomes $-(x+5)=5x+2$

STEP 3

Now, let's solve the equation from Case1.
$3x+5=5x+2$ Subtract $3x$ from both sides $5=2x+2$

STEP 4

Subtract2 from both sides of the equation $3=2x$

STEP 5

Divide both sides of the equation by2 $x=\frac{3}{2}$

STEP 6

Now, let's solve the equation from Case2.
$-(3x+5)=5x+2$ Multiply out the negative sign on the left side $-3x-5=5x+2$

STEP 7

Add $3x$ to both sides of the equation $-5=x+2$

STEP 8

Subtract2 from both sides of the equation $-7=8x$

STEP 9

Divide both sides of the equation by8 $x=-\frac{7}{8}$

STEP 10

So, the solutions to the equation $|3x+5|=5x+2$ are $x=\frac{3}{2}$ and $x=-\frac{7}{8}$ .

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