# Linear Equations

Solve the equation

Find the common denominator and multiply both sides of the equation by it.

 Add −5x to both sides of the equation. Find the common denominator Add −10 to both sides of the equation. Multiply both sides of the equation by Multiply by the reciproca

Solve the equation

Find the common denominator and multiply both sides of the equation by it.

 Distribute to remove the parenthesis. Collect like terms Add 25 to both sides. Multiply both sides by

The formula W= 0.3x + 46.6 models the average number of hours worked by
American workers per week when W is the hours worked and x is the number of
years since 1980. When will we average 55 hours per week?

The average American is probably working 55 hours per week now, 28 years after 1980.

 Einstein’s formula E = mc2, relates energy and mass with the speed of light. E represents energy in ergs, m represents mass in grams, and c is the speed of light in centimeters per second. The speed of light in a vacuum is 3 × 1010 meters per second. The square of 3 × 1010 is 9 × 1020 . 1 gram of matter will contain 9 × 1020 ergs of energy. The energy in 1 gram of matter could move another gram of matter 559,234,073,013,000 miles at a rate of 1 centimeter per second.

Solve the equation E = mc2 for m.

Solve the equation E = mc2 for c2.

P= 2l+2w is the formula for calculating the perimeter of a
rectangle. l represents the length of a side of the rectangle and
w represents the width.

Solve P= 2l+2wfor w.

Multiply both sides by

 Solve the equation 3x + 7y = 21 for x Solve the equation 3x + 7y = 21 for y Subtract 7y from both sides Subtract 3x from both sides 3x + 7y – 7y = 21 – 7y 3x – 3x + 7y = 21 – 3x 3x = 21 – 7y 7y = 21 – 3x Divide both sides by 3 Divide both sides by 7

The distance a car will travel is calculated with the formula d= rt,
where d is the distance traveled, r is the rate of travel and t is the
time traveling.

How far will the car travel at a rate of 75 miles per hour in 3
hours?

How long will the it take the car to travel 175 miles at a rate of 75
miles per hour?

How fast was the car traveling if it went 390 miles in 5 hours?

 Solve the equation 3x+ 6 = 3(x+ 5) Solve the equation -2x+ 5x–18 = -3x + 6(x–3) Distribute Distribute 3x+ 6 = 3x+ 15 –2x+ 5x–18 = –3x + 6x–18 Subtract3xfrom both sides Combine like terms 6 = 15 3x–18 = 3x –18 This is never true. There is no solution . This is a contradiction. This is always true. There are infinitely many solutions . This is an identity.
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