Grade 8: Translating Equations

Grade 8: Translating Equations

Read each question carefully and follow the instructions. Show your work where applicable.

Translate the following verbal expressions into algebraic equations. Use 'x' for the unknown number.

1. The sum of a number and five is twelve:  

2. Seven less than twice a number is nine:  

3. The product of a number and three, increased by four, is twenty-five:  

4. Half of a number decreased by one is ten:  

5. Six times a number is equal to forty-two:  

Translate the following algebraic equations into verbal expressions.

1. x + 8 = 15:  

2. 4y - 3 = 13:  

3. (n/2) + 6 = 11:  

4. 5(z - 2) = 20:  

For each word problem, write an algebraic equation and then solve it.

1. Sarah bought a book for $12 and three pens. If her total bill was $21, how much did each pen cost?

Equation:

Solution:

2. A number is multiplied by 4, and then 5 is subtracted from the product. The result is 19. What is the number?

Equation:

Solution:

Choose the correct algebraic equation for each verbal expression.

1. Ten more than a number is equal to twenty-three.

2. The quotient of a number and 4 is 8.

Determine if the translation from words to equations is True or False.

1. "Three times a number decreased by five is ten" translates to 3x - 5 = 10.

2. "The difference between a number and seven is fourteen" translates to 7 - x = 14.