Simplify 4(x + 5) − (3x + 10) − 2x + 5.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

1) Evaluate $\left(\frac{80}{640}\right)^{\frac{2}{3}}$

Simplify the fraction inside the parenthesis.
$\frac{80}{640} = \frac{8}{64} = \frac{1}{8}$
So the expression becomes:
$\left(\frac{1}{8}\right)^{\frac{2}{3}}$
Apply the fractional exponent.
The exponent $\frac{2}{3}$ means taking the cube root first, then squaring the result.
$\left(\frac{1}{8}\right)^{\frac{2}{3}} = \left(\sqrt[3]{\frac{1}{8}}\right)^2$
Calculate the cube root.
$\sqrt[3]{\frac{1}{8}} = \frac{\sqrt[3]{1}}{\sqrt[3]{8}} = \frac{1}{2}$
So the expression becomes:
$\left(\frac{1}{2}\right)^2$
Square the result.
$\left(\frac{1}{2}\right)^2 = \frac{1^2}{2^2} = \frac{1}{4}$
The evaluated value is $\boxed{\frac{1}{4}}$ .

2) Simplify $4(x+5) - (3x+10) - 2x + 5$
Distribute the 4 into the first parenthesis and distribute the negative sign into the second parenthesis.
$4(x+5) = 4x + 20$ $-(3x+10) = -3x - 10$
The expression becomes:
$4x + 20 - 3x - 10 - 2x + 5$
Group the like terms (terms with $x$ and constant terms).
$(4x - 3x - 2x) + (20 - 10 + 5)$
Combine the like terms.
$(4x - 3x - 2x) = (1x - 2x) = -1x = -x$ $(20 - 10 + 5) = (10 + 5) = 15$
The simplified expression is:
$\boxed{-x + 15}$

Simplify 4(x + 5) - (3x + 10) - 2x + 5.