Answer:
[tex]x=7 \quad \text{or} \quad x=-\dfrac{17}{3}[/tex]
Step-by-step explanation:
The absolute value of a number is its positive numerical value.
Given equation:
[tex]|3x-2| = 19[/tex]
To solve an equation containing an absolute value, first isolate the absolute value on one side of the equation. (This has already been done).
Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, and solve both equations:
[tex]\begin{aligned}\text{\underline{Equation 1}} &&\quad && \text{\underline{Equation 2}}\\3x-2 & = 19 && & 3x-2&=-19\\3x-2+2 & = 19+2 && & 3x-2+2&=-19+2\\3x&=21 &&& 3x&=-17\\\dfrac{3x}{3}&=\dfrac{21}{3} &&& \dfrac{3x}{3}&=-\dfrac{17}{3}\\x&=7 &&& x&=-\dfrac{17}{3}\end{aligned}[/tex]
Check the solutions by substituting each found value of x into the original equation:
[tex]\begin{aligned}x=7 \implies |3(7)-2|&=19\\|21-2|&=19\\|19|&=19\\19&=19\end{aligned}[/tex]
[tex]\begin{aligned}x=-\dfrac{17}{3} \implies \left|3\left(-\dfrac{17}{3}\right)-2\right|&=19\\|-17-2|&=19\\|-19|&=19\\19&=19\end{aligned}[/tex]
Therefore, this verifies that both solutions are valid.
To show the solutions on a number line (attached):
- Place a closed circle at x = 7.
- Place a closed circle at x = -¹⁷/₃ = -5 ²/₃
