Isolate absolute value expression: First, we need to isolate the absolute value expression on one side of the equation. We start by adding 1 to both sides of the equation to get rid of the -1 on the left side. -2|2x+12|-1+1 = -17+1 -2|2x+12| = -16Divide by -2: Next, we divide both sides of the equation by -2 to solve for the absolute value expression. -2|2x+12| / -2 = -16 / -2 |2x+12| = 8Absolute value equation: Now we have an absolute value equation |2x+12| = 8. This means that the expression inside the absolute value, 2x+12, can either be 8 or -8. So we have two separate equations to solve: 2x + 12 = 8 and 2x + 12 = -8Solve first equation: Let's solve the first equation: 2x + 12 = 8. Subtract 12 from both sides to isolate the term with x. 2x + 12 - 12 = 8 - 12 2x = -4Divide by 2: Now, divide both sides by 2 to solve for x. 2x / 2 = -4 / 2 x = -2Solve second equation: Next, we solve the second equation: 2x + 12 = -8. Subtract 12 from both sides to isolate the term with x. 2x + 12 - 12 = -8 - 12 2x = -20Divide both sides by 2 to solve for x. 2x / 2 = -20 / 2 x = -10

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$-2|2 x+12|-1=-17$

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Math Problems

Grade 6

Integer inequalities with absolute values

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-2|2 x+12|-1=-17

Isolate absolute value expression: First, we need to isolate the absolute value expression on one side of the equation. We start by adding $1$ to both sides of the equation to get rid of the $-1$ on the left side. $\newline$ $-2|2x+12|-1+1 = -17+1$ $\newline$ $-2|2x+12| = -16$
Divide by $-2$ : Next, we divide both sides of the equation by $-2$ to solve for the absolute value expression. $\newline$ $-2|2x+12| / -2 = -16 / -2$ $\newline$ $|2x+12| = 8$
Absolute value equation: Now we have an absolute value equation $|2x+12| = 8$ . This means that the expression inside the absolute value, $2x+12$ , can either be $8$ or $-8$ . $\newline$ So we have two separate equations to solve: $\newline$ $2x + 12 = 8$ and $2x + 12 = -8$
Solve first equation: Let's solve the first equation: $2x + 12 = 8$ . Subtract $12$ from both sides to isolate the term with $x$ . $2x + 12 - 12 = 8 - 12$ $2x = -4$
Divide by $2$ : Now, divide both sides by $2$ to solve for $x$ . $\frac{2x}{2} = \frac{-4}{2}$ $x = -2$
Solve second equation: Next, we solve the second equation: $2x + 12 = -8$ . Subtract $12$ from both sides to isolate the term with $x$ . $2x + 12 - 12 = -8 - 12$ $2x = -20$
Solve second equation: Next, we solve the second equation: $2x + 12 = -8$ . Subtract $12$ from both sides to isolate the term with $x$ . $2x + 12 - 12 = -8 - 12$ $2x = -20$ Divide both sides by $2$ to solve for $x$ . $\frac{2x}{2} = \frac{-20}{2}$ $x = -10$