Answered

Get expert insights and reliable answers to your questions on IDNLearn.com. Find reliable solutions to your questions quickly and easily with help from our experienced experts.

Rewrite the following expression to solve for [tex]\(x\)[/tex]:

[tex]\[4x + 2(2x - 5) = (x - 3) - (x - 8)\][/tex]

Note: The expression [tex]\((2m - 3n) 2\)[/tex] seems incomplete and does not logically fit with the equation provided.

Sagot :

GinnyAnsweridn
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].
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.