Question

answer the following questions and be sure to show all of your work. you may use a calculator.

1. using the given key and equation mat, represent and solve the following linear equation algebraically. then, confirm your solution.

4d = -12
key
□ = 1 ■ = -1
▭ = d ▬ = -d
equation mat
two rectangles with = between them

1. write the equation represented by the illustration below. then, find the solution.

two dark rectangles with x inside = four light squares with 1 inside
equation: _____________

1. which operation would be used to solve the equation below?

-3g = 30
a) multiply by 3 on both sides of the equation
b) divide by 3 on both sides of the equation
c) multiply by -3 on both sides of the equation
d) divide by -3 on both sides of the equation

1. write an algebraic expression to represent the following verbal phrases.

the difference of a number (n) and 14 _____________
the sum of a number (x) and negative six _____________
the quotient of 15 and a number (c) _____________

Explanation:

Question 1

Step1: Solve the equation \(4d = -12\)

To solve for \(d\), we divide both sides of the equation by 4.
\(\frac{4d}{4}=\frac{-12}{4}\)

Step2: Simplify both sides

Simplifying the left side, \(\frac{4d}{4}=d\). Simplifying the right side, \(\frac{-12}{4}=-3\). So \(d = - 3\).

Step3: Confirm the solution

Substitute \(d=-3\) back into the original equation: Left side \(4\times(-3)=-12\), right side is \(-12\). Since left side = right side, the solution is correct.

Step1: Write the equation

From the illustration, we have 2 rectangles with \(x\) (so \(2x\)) equal to 4 small squares (each representing 1, so 4). So the equation is \(2x = 4\).

Step2: Solve the equation

Divide both sides by 2: \(\frac{2x}{2}=\frac{4}{2}\), which gives \(x = 2\).

To solve the equation \(-3g=30\) for \(g\), we need to isolate \(g\). Since \(g\) is multiplied by \(-3\), we use the inverse operation of multiplication, which is division. So we divide both sides of the equation by \(-3\).

Answer:

The solution of the equation \(4d=-12\) is \(d = - 3\)

Question 2