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# Solving Multi-Step Equations

## Solving Multi-Step Equations 1.14 - Solution

a
To determine the number of possible solutions, we should solve the equation for $r.$ Let's start with multiplying both sides by $3.$ This way, we get an equivalent equation without fractions.
$2(4r+6)=\dfrac{2}{3}(12r+18)$
$6(4r+6)=2(12r+18)$
$24r+36=2(12r+18)$
$24r+36=24r+36$
Rewriting the equation resulted in the same expression on both sides. Thus, the equality holds true for all values of $r.$ Therefore, the equation has infinitely many solutions.
b
On the left-hand side, we have a product of $5$ and a parenthetical expression. To evaluate this product, we distribute $5$ to each term in the parentheses. Then we can continue solving the equation.
$n+5(n-1)=7$
$n+5n-5=7$
$6n-5=7$
$6n=12$
$n=2$
Thus, the equation has one solution.
c
To solve this equation for $y,$ we need to remember that when removing a negative parentheses we need to change signs on the terms inside. We will then combine like terms to isolate $y.$
$8y-(2y-3)=12$
$8y-2y+3=12$
$6y+3=12$
$6y=9$
$y=\dfrac{9}{6}$
The equation has one solution.