Solve the equation. Write a justification for each step. (x+4)/(3) = -10 A. (x+4)/(3) = -10 Given x+4 =-13 Mult. Prop. of = x=-17 Subtr. Prop. of = B. (x+4)/(3) = -10 Given x+4=…

Question

Solve the equation. Write a justification for each step.


`(x+4)/(3)` = -10

A.
`(x+4)/(3)` = -10 Given
x+4 =-13 Mult. Prop. of =
x=-17 Subtr. Prop. of =
B.
`(x+4)/(3)` = -10 Given
x+4=−30 Mult. Prop. of =
x=-34 Subtr. Prop of =
C.
`(x+4)/(3)` = -10 Given
x+4=-13 Reflex. Prop. of =
x=-17 Add. Prop. of =
D.
`(x+4)/(3)` = -10 Given
x+4=-30 Div. Prop. of =
x=-34 Sym. Prop. of=

Answer 1

Explanation:

We have (x + 4)/3 = -10.

=> x + 4 = -30 (Multiplication Property)

=> x = -34 (Subtraction Property).

The answer is B.

Answer 2

`\begin{aligned}\textsf{B.}\quad (x+4)/(3)&=-10 \qquad \textsf{Given}\\\\x+4&=-30 \qquad \textsf{Multiplication Property of Equality}\\\\x&=-34 \qquad \textsf{Subtraction Property of Equality}\\\\\end{aligned}`

Explanation:

Given equation:

`(x+4)/(3)=-10`

To solve the given equation, start by multiplying both sides of the equation by 3 to eliminate the fraction.

This is done using the multiplication property of equality, which states that both sides of an equation can be multiplied by the same non-zero number without altering the equality.

`(x+4)/(3) \cdot 3 = -10 \cdot 3`

`x+4 = -30`

Now, isolate x on one side of the equation by subtracting 4 from both sides of the equation.

This is done using the subtraction property of equality, which states that the equality remains unchanged when the same value is subtracted from both sides of an equation.

`x + 4 - 4 = -30 - 4`

`x = -34`

So, the solution to the equation x = -34.