Solve for all values of x in simplest form. |-5x+14|=3 Answer: x=

Understand absolute value equation: Understand the absolute value equation |-5x + 14| = 3. The absolute value of a number is its distance from zero on the number line, which means it is always non-negative. Therefore, the equation |-5x + 14| = 3 means that the expression inside the absolute value, -5x + 14, is either 3 or -3.Set up two equations: Set up two separate equations to solve for x. Since -5x + 14 can be either 3 or -3, we write two equations: 1) -5x + 14 = 3 2) -5x + 14 = -3Solve first equation: Solve the first equation -5x + 14 = 3. Subtract 14 from both sides to isolate the term with x: -5x + 14 - 14 = 3 - 14 -5x = -11 Now, divide both sides by -5 to solve for x: x = -11 / -5 x = 11/5Solve second equation: Solve the second equation -5x + 14 = -3. Subtract 14 from both sides to isolate the term with x: -5x + 14 - 14 = -3 - 14 -5x = -17 Now, divide both sides by -5 to solve for x: x = -17 / -5 x = 17/5

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Solve for all values of
x in simplest form.

|-5x+14|=3
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $|-5 x+14|=3$ $\newline$ Answer: $x=$

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Math Problems

Grade 8

Evaluate absolute value expressions

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

|-5 x+14|=3

\newline

Answer:

x=

Understand absolute value equation: Understand the absolute value equation |-5x + 14| = 3\. The absolute value of a number is its distance from zero on the number line, which means it is always non-negative. Therefore, the equation \$|-5x + 14| = 3 means that the expression inside the absolute value, $-5x + 14$ , is either $3$ or $-3$ .
Set up two equations: Set up two separate equations to solve for $x$ . Since $-5x + 14$ can be either $3$ or $-3$ , we write two equations: $1$ ) $-5x + 14 = 3$ $2$ ) $-5x + 14 = -3$
Solve first equation: Solve the first equation $-5x + 14 = 3$ . $\newline$ Subtract $14$ from both sides to isolate the term with $x$ : $\newline$ $-5x + 14 - 14 = 3 - 14$ $\newline$ $-5x = -11$ $\newline$ Now, divide both sides by $-5$ to solve for $x$ : $\newline$ $x = -11 / -5$ $\newline$ $x = 11/5$
Solve second equation: Solve the second equation $-5x + 14 = -3$ . $\newline$ Subtract $14$ from both sides to isolate the term with x: $\newline$ $-5x + 14 - 14 = -3 - 14$ $\newline$ $-5x = -17$ $\newline$ Now, divide both sides by $-5$ to solve for x: $\newline$ $x = -17 / -5$ $\newline$ $x = 17/5$