Solve the following equations for y: 10 − 3y + 4 = 8 + 4y − y and 2(y + 1) = 10 − 2(3y − 4).

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the problems:

Combine like terms on both sides of the equation.
$(10 + 4) - 3y = 8 + (4y - y)$ $14 - 3y = 8 + 3y$
Add $3y$ to both sides of the equation.
$14 = 8 + 3y + 3y$ $14 = 8 + 6y$
Subtract 8 from both sides of the equation.
$14 - 8 = 6y$ $6 = 6y$
Divide both sides by 6 to solve for $y$ .
$y = \frac{6}{6}$ $y = 1$
The solution is $\boxed{\text{}y = 1\text{}}$

3.4.3
Distribute the numbers into the parentheses on both sides of the equation.
$2(y) + 2(1) = 10 - 2(3y) - 2(-4)$ $2y + 2 = 10 - 6y + 8$
Combine constant terms on the right side of the equation.
$2y + 2 = (10 + 8) - 6y$ $2y + 2 = 18 - 6y$
Add $6y$ to both sides of the equation.
$2y + 6y + 2 = 18$ $8y + 2 = 18$
Subtract 2 from both sides of the equation.
$8y = 18 - 2$ $8y = 16$
Divide both sides by 8 to solve for $y$ .
$y = \frac{16}{8}$ $y = 2$
The solution is $\boxed{\text{}y = 2\text{}}$

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