Solve the equation for all values of x. |4x+9|-9=2x Answer: x=

Isolate absolute value: We have the equation |4x+9|-9=2x. To solve for x, we first need to isolate the absolute value expression on one side of the equation. Add 9 to both sides of the equation to isolate the absolute value. |4x+9| - 9 + 9 = 2x + 9 |4x+9| = 2x + 9Split into two cases: Now we have |4x+9| = 2x + 9. The absolute value equation can be split into two separate equations, because if |A| = B, then A = B or A = -B. So we have two cases: Case 1: 4x + 9 = 2x + 9 Case 2: 4x + 9 = -(2x + 9)Solve Case 1: Solve Case 1. 4x + 9 = 2x + 9 Subtract 2x from both sides to isolate x on one side. 4x - 2x + 9 = 2x - 2x + 9 2x + 9 = 9 Subtract 9 from both sides. 2x + 9 - 9 = 9 - 9 2x = 0 Divide by 2. x = 0 / 2 x = 0Solve Case 2: Solve Case 2. 4x + 9 = -(2x + 9) Distribute the negative sign on the right side. 4x + 9 = -2x - 9 Add 2x to both sides to get all x terms on one side. 4x + 2x + 9 = -2x + 2x - 9 6x + 9 = -9 Subtract 9 from both sides. 6x + 9 - 9 = -9 - 9 6x = -18 Divide by 6. x = -18 / 6 x = -3

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Solve the equation for all values of
x.

|4x+9|-9=2x
Answer:
x=

Solve the equation for all values of $x$ . $\newline$ $|4 x+9|-9=2 x$ $\newline$ Answer: $x=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve the equation for all values of

x

\newline

|4 x+9|-9=2 x

\newline

Answer:

x=

Isolate absolute value: We have the equation $|4x+9|-9=2x$ . To solve for x, we first need to isolate the absolute value expression on one side of the equation. $\newline$ Add $9$ to both sides of the equation to isolate the absolute value. $\newline$ $|4x+9| - 9 + 9 = 2x + 9$ $\newline$ $|4x+9| = 2x + 9$
Split into two cases: Now we have $|4x+9| = 2x + 9$ . The absolute value equation can be split into two separate equations, because if $|A| = B$ , then $A = B$ or $A = -B$ . $\newline$ So we have two cases: $\newline$ Case $1$ : $4x + 9 = 2x + 9$ $\newline$ Case $2$ : $4x + 9 = -(2x + 9)$
Solve Case $1$ : Solve Case $1$ . $\newline$ $4x + 9 = 2x + 9$ $\newline$ Subtract $2x$ from both sides to isolate $x$ on one side. $\newline$ $4x - 2x + 9 = 2x - 2x + 9$ $\newline$ $2x + 9 = 9$ $\newline$ Subtract $9$ from both sides. $\newline$ $2x + 9 - 9 = 9 - 9$ $\newline$ $2x = 0$ $\newline$ Divide by $2$ . $\newline$ $x = 0 / 2$ $\newline$ $2x$ $0$
Solve Case $2$ : Solve Case $2$ . $\newline$ $4x + 9 = -(2x + 9)$ $\newline$ Distribute the negative sign on the right side. $\newline$ $4x + 9 = -2x - 9$ $\newline$ Add $2x$ to both sides to get all $x$ terms on one side. $\newline$ $4x + 2x + 9 = -2x + 2x - 9$ $\newline$ $6x + 9 = -9$ $\newline$ Subtract $9$ from both sides. $\newline$ $6x + 9 - 9 = -9 - 9$ $\newline$ $6x = -18$ $\newline$ Divide by $6$ . $\newline$ $4x + 9 = -2x - 9$ $0$ $\newline$ $4x + 9 = -2x - 9$ $1$