Let's solve the given equation step-by-step:
The equation is:
[tex]\[4x + 2(2x - 5) = (x - 3) - (x - 8)\][/tex]
1. Let's simplify both sides of the equation.
Left Side:
[tex]\[4x + 2(2x - 5)\][/tex]
First, distribute 2 inside the parentheses:
[tex]\[= 4x + 2 \cdot 2x - 2 \cdot 5\][/tex]
[tex]\[= 4x + 4x - 10\][/tex]
Now combine like terms:
[tex]\[= 8x - 10\][/tex]
Right Side:
[tex]\[(x - 3) - (x - 8)\][/tex]
Distribute the subtraction across the parentheses:
[tex]\[= x - 3 - x + 8\][/tex]
Combine like terms:
[tex]\[= 5\][/tex]
2. Now set the simplified left side equal to the simplified right side:
[tex]\[8x - 10 = 5\][/tex]
3. Solve for [tex]\(x\)[/tex] by isolating the term with [tex]\(x\)[/tex]:
[tex]\[8x - 10 + 10 = 5 + 10\][/tex]
[tex]\[8x = 15\][/tex]
4. Divide both sides by 8:
[tex]\[x = \frac{15}{8}\][/tex]
5. Simplify the fraction:
[tex]\[x = 1.875\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is:
[tex]\[x = 1.875\][/tex]
So, upon solving the equation step-by-step, we find that [tex]\(x = 1.875\)[/tex].
