Examples with solutions for The Distributive Property for 7th Grade: Using variables

Exercise #1

(7x+3)×(10+4)=238 (7x+3)\times(10+4)=238

Video Solution

Step-by-Step Solution

We begin by solving the addition exercise in the right parenthesis:

(7x+3)+14=238 (7x+3)+14=238

We then multiply each of the terms inside of the parentheses by 14:

(14×7x)+(14×3)=238 (14\times7x)+(14\times3)=238

Following this we solve each of the exercises inside of the parentheses:

98x+42=238 98x+42=238

We move the sections whilst retaining the appropriate sign:

98x=23842 98x=238-42

98x=196 98x=196

Finally we divide the two parts by 98:

9898x=19698 \frac{98}{98}x=\frac{196}{98}

x=2 x=2

Answer

2

Exercise #2

(9+17x)×(6+1)=420 (9+17x)\times(6+1)=420

Calculate a X

Video Solution

Step-by-Step Solution

We begin by solving the addition exercise in the right parenthesis:

(9+17x)×7=420 (9+17x)\times7=420

We then multiply each of the terms inside the parentheses by 7:

(9×7)+(17x×7)=420 (9\times7)+(17x\times7)=420

We continue by solving each of the exercises inside of the parentheses:

63+119x=420 63+119x=420

Following this we rearrange the sections whilst maintaining the appropriate sign:

119x=42063 119x=420-63

119x=357 119x=357

Finally we divide the two parts by 119:

119119x=357119 \frac{119}{119}x=\frac{357}{119}

x=3 x=3

Answer

3

Exercise #3

(a+3a)×(5+2)=112 (a+3a)\times(5+2)=112

Calculate a a

Video Solution

Step-by-Step Solution

We begin by solving the two exercises inside of the parentheses:

4a×7=112 4a\times7=112

We then divide each of the sections by 4:

4a×74=1124 \frac{4a\times7}{4}=\frac{112}{4}

In the fraction on the left side we simplify by 4 and in the fraction on the right side we divide by 4:

a×7=28 a\times7=28

Remember that:

a×7=a7 a\times7=a7

Lastly we divide both sections by 7:

a77=287 \frac{a7}{7}=\frac{28}{7}

a=4 a=4

Answer

4

Exercise #4

A building is 21 meters high, 15 meters long, and 14+30X meters wide.

Express its volume in terms of X.

(14+30X)(14+30X)(14+30X)212121151515

Step-by-Step Solution

We use a formula to calculate the volume: height times width times length.

We rewrite the exercise using the existing data:

21×(14+30x)×15= 21\times(14+30x)\times15=

We use the distributive property to simplify the parentheses.

We multiply 21 by each of the terms in parentheses:

(21×14+21×30x)×15= (21\times14+21\times30x)\times15=

We solve the multiplication exercise in parentheses:

(294+630x)×15= (294+630x)\times15=

We use the distributive property again.

We multiply 15 by each of the terms in parentheses:

294×15+630x×15= 294\times15+630x\times15=

We solve each of the exercises in parentheses to find the volume:

4,410+9,450x 4,410+9,450x

Answer

4410+9450x 4410+9450x

Exercise #5

Look at the rectangle in the figure.

What is its area?

Video Solution

Step-by-Step Solution

We know that the area of a rectangle is equal to its length multiplied by its width.

We begin by writing an equation with the available data.

(4x+x2)×(3x+8+5x) (4x+x^2)\times(3x+8+5x)

Next we use the distributive property to solve the equation.

(4x×3x)+(4x×8)+(4x×5x)+(x2×3x)+(x2×8)+(x2×5x)= (4x\times3x)+(4x\times8)+(4x\times5x)+(x^2\times3x)+(x^2\times8)+(x^2\times5x)=

We then solve each of the exercises within the parentheses:

12x2+32x+20x2+3x3+16x2+5x3= 12x^2+32x+20x^2+3x^3+16x^2+5x^3=

Finally we add up all the coefficients of X squared and all the coefficients of X cubed and we obtain the following:

48x2+8x3+32x 48x^2+8x^3+32x

Answer

8x3+28x2+44x 8x^3+28x^2+44x

Exercise #6

Gerard plans to paint a fence 7X meters high and 30X+4 meters long.

Gerardo paints at a rate of 7 m² per half an hour.

Choose the expression that represents the time it takes for Gerardo to paint one side of the fence.

30X+430X+430X+47X7X7X

Video Solution

Step-by-Step Solution

In order to solve the exercise, we first need to know the total area of the fence.

Let's remember that the area of a rectangle equals length times width.

Let's write the exercise according to the given data:

7x×(30x+4) 7x\times(30x+4)

We'll use the distributive property to solve the exercise. That means we'll multiply 7x by each term in the parentheses:

(7x×30x)+(7x×4)= (7x\times30x)+(7x\times4)=

Let's solve each term in the parentheses and we'll get:

210x2+28x 210x^2+28x

Now to calculate the painting time, we'll use the formula:

7m212hr=14m2hr \frac{7m^2}{\frac{1}{2}hr}=14\frac{m^2}{hr}

The time will be equal to the area divided by the work rate, meaning:

210x2+28x14 \frac{210x^2+28x}{14}

Let's separate the exercise into addition between fractions:

210x214+28x14= \frac{210x^2}{14}+\frac{28x}{14}=

We'll reduce by 14 and get:

15x2+2x 15x^2+2x

And this is Isaac's work time.

Answer

15x2+2x 15x^2+2x hours