4.6(2r+16) − 2(5r+6)

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems you sent:

1) Simplify the expression: $4(x+y)$

Distribute the 4 to both terms inside the parentheses.
$4(x+y) = 4 \cdot x + 4 \cdot y$
Perform the multiplication.
$4x + 4y$
The simplified expression is $\boxed{4x+4y}$ .

2) Simplify the expression: $3\left(\frac{4}{3}x+5\right)$
Distribute the 3 to both terms inside the parentheses.
$3\left(\frac{4}{3}x+5\right) = 3 \cdot \frac{4}{3}x + 3 \cdot 5$
Perform the multiplication.
$4x + 15$
The simplified expression is $\boxed{4x+15}$ .

3) Solve the equation: $8(4x-15) = 4(2x+12)$
Distribute the numbers on both sides of the equation.
$8 \cdot 4x - 8 \cdot 15 = 4 \cdot 2x + 4 \cdot 12$ $32x - 120 = 8x + 48$
Subtract $8x$ from both sides of the equation.
$32x - 8x - 120 = 8x - 8x + 48$ $24x - 120 = 48$
Add 120 to both sides of the equation.
$24x - 120 + 120 = 48 + 120$ $24x = 168$
Divide both sides by 24 to solve for $x$ .
$x = \frac{168}{24}$ $x = 7$
The solution is $\boxed{x=7}$ .

4) Simplify the expression: $6(2x+16) - 2(3x+6)$
Distribute the 6 into the first set of parentheses and the -2 into the second set of parentheses.
$6 \cdot 2x + 6 \cdot 16 - 2 \cdot 3x - 2 \cdot 6$ $12x + 96 - 6x - 12$
Combine like terms ( $x$ terms and constant terms).
$(12x - 6x) + (96 - 12)$ $6x + 84$
The simplified expression is $\boxed{6x+84}$ .

4.6(2r+16) - 2(5r+6)