# Integers and Equations using the Multiplication Principle

See attached

Solve using the Multiplication principle.

Determine whether 24 is a solution of the equation;

Translate to an algebraic expression

Solve using the addition principle

https://brainmass.com/math/basic-algebra/integers-equations-using-multiplication-principle-239485

#### Solution Preview

1.

Solve using the Multiplication principle. Don't forget to check.

-17x=187

Solution:

Divide each side by -17

=> x = 187/-17 = -11

Check:

Substitute x = -11, we will get

-17(-11) = 187

Thus it is correct.

2.

Determine whether 24 is a solution of the equation; x+11=33; Is 24 a solution? Yes or NO

N0, because 24 + 11 = 43

Solve using the principle don't forget to check: 2x-14=2

The solution is x=

2x-14=2

Add 14 to each side

2x = 16

ïƒ° x = 8

Substitute x = 8 in given equation

2(8) - 14 = 16 -14 = 2

Thus, it satisfies the given equation.

The solution is x = 8.

3. Solve : 5(x-6) + 4= 7(x+2)-8

5x - 30 + 4 = 7x + 14 - 8

5x - 26 = 7x + 6

5x - 7x = 6 + 26

-2x = 32

=> x = 32/-2 = -16

4. Simplify; [3-8(7-8)]

= [ 3 - 8(-1)] = 3 + 8 = 11

5. Translate to an algebraic expression; The product of 38% and some number

The ...

#### Solution Summary

This provides examples of working with algebra problems, including solving equations, writing algebraic expressions, and performing operations on positive and negative integers.