Question

complete the process of solving the equation. fill in all missing terms and select all missing descriptions. simplify any fractions. -5(3r - 1) - 19 = -14r - 11 -15r + - 19 = -14r - 11 apply the distributive property -15r - = -14r - 11 combine like terms - 14 = -11 add 14r to both sides -r = r =

Explanation:

Step1: Apply distributive property

We know that $-5(3r - 1)=-5\times3r-5\times(- 1)=-15r + 5$. So the equation $-5(3r - 1)-19=-14r - 11$ becomes $-15r+5 - 19=-14r - 11$.

Step2: Combine like terms

Combine the constant terms on the left - hand side. $5-19=-14$, so the equation is $-15r-14=-14r - 11$.

Step3: Add 14r to both sides

$(-15r-14)+14r=(-14r - 11)+14r$. This simplifies to $-15r + 14r-14=-14r+14r - 11$, or $-r-14=-11$.

Step4: Add 14 to both sides

$(-r-14)+14=(-11)+14$. We get $-r=3$.

Step5: Multiply both sides by - 1

$(-1)\times(-r)=(-1)\times3$. So $r=-3$.

Answer:

The missing terms and descriptions are:

• In the first step after applying the distributive property, the missing term is $5$.
• In the second step after combining like terms, the equation is $-15r - 14=-14r - 11$ (the missing term on the left - hand side is $14$).
• After adding $14r$ to both sides, we have $-r-14=-11$.
• After adding 14 to both sides, $-r = 3$.
• After multiplying both sides by - 1, $r=-3$.