Answer:
x= -3
Step-by-step explanation:
[tex]2(2x + 3) = x - 3 \\ 4x + 6 = x - 3 \\ 4x = x - 3 - 6 \\ 4x - x = - 3 - 6 \\ 3x = - 9 \\ x = \frac{ - 9}{3} \\ x = - 3[/tex]
Answer:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Step-by-step explanation:
Given absolute value equation:
[tex]2|2x+3|=|x-3|[/tex]
The absolute value of a number is its positive numerical value.
Therefore, the expressions inside the bars should be set to both positive and negative. Rewrite the absolute value equation as four equations without absolute value bars and simplify:
[tex]\textsf{Positive = Positive}: \quad 2(2x+3)=x-3[/tex]
[tex]\textsf{Positive = Negative}: \quad 2(2x+3)=-(x-3)[/tex]
[tex]\begin{aligned}\textsf{Negative = Positive}: \quad -2(2x+3) &=x-3\\ \implies 2(2x+3) &=-(x-3)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Negative = Negative}: \quad -2(2x+3) &=-(x-3)\\ \implies 2(2x+3)&=x-3\end{aligned}[/tex]
From inspection of the equations:
so there are only two unique equations to be solved.
Equation 1
[tex]\begin{aligned}2(2x+3) & =x-3\\4x+6 & = x-3\\4x+6-x&=x-3-x\\3x+6&=-3\\3x+6-6&=-3-6\\3x & =-9\\\dfrac{3x}{3} & = \dfrac{-9}{3}\\ x&=-3 \end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}2(2x+3)&=-(x-3)\\4x+6&=-x+3\\4x+6+x&=-x+3+x\\5x+6&=3\\5x+6-6&=3-6\\5x &=-3\\ \dfrac{5x}{5}&=\dfrac{-3}{5}\\x &=-\dfrac{3}{5} \end{aligned}[/tex]
Therefore, the solutions are:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
