Pre-Algebra Demystified

SOLUTION 5 ð2xþ3yÞ¼ 5 2xþ 5 3y ¼10xþ15y EXAMPLE Multiply 8(xþ3y). SOLUTION 8 ðxþ3yÞ¼ 8 1xþ 8 3y ¼8xþ24y The distributive pro ...

Math Note: The distributive property is called the distributive property for multiplication over addition. PRACTICE Multiply eac ...

To add or subtract like terms, add or subtract the numerical coefficients and use the same variables. EXAMPLE Add 7yþ3y. SOLUTIO ...

Math Note: An algebraic expression of the form aþ(
b) is usually written as a
b. PRACTICE For each of the following expressions, ...

EXAMPLE Simplify 5(2xþ3)
6. SOLUTION 5 ð2xþ 3 Þ
6 ¼10xþ 15
6 Remove parentheses ¼10xþ 9 Combine like terms EXAMPLE Simplify
2 ...

i.e., substitute the values of the variables in the formula and simplify using the order of operations. EXAMPLE Find the Fahrenh ...

ANSWERS 120 miles 25o 216 cubic inches 20 feet 4 amperes Solving Simple Equations Anequationis a statement of equality of two ...

SOLUTION x
8 ¼ 22 x
8 þ 8 ¼ 22 þ8 Add 8 to both sides x
0 ¼ 30 x¼ 30 Check: x
8 ¼ 22 30
8 ¼ 22 22 ¼ 22 An equation such as ...

SOLUTION 7x¼ 28 7 x 7 ¼ 28 7 Divide both sides by 7 x¼ 4 Check: 7x¼ 28 7 ð 4 Þ¼ 28 28 ¼ 28 An equation such as x 3 ¼15 can be so ...

traction are opposite operations and multiplication and division are oppo- site operations. PRACTICE Solve each of the following ...

SOLUTION 8xþ 5 ¼ 37 8xþ 5
5 ¼ 37
5 Subtract 5 8x¼ 32 8 x 8 ¼ 32 8 x¼ 4 Check: 8xþ 5 ¼ 37 8 ð 4 Þþ 5 ¼ 37 32 þ 5 ¼ 37 37 ¼ 37 ...

SOLUTION
3xþ 12 ¼
36
3xþ 12
12 ¼
36
12 Subtract 12
3x¼
48
3 x
3 ¼
48
3 Divide by
3 x¼ 16 Check:
3xþ 12 ¼
36 ...

SOLUTION 2xþ 5 þ3x¼ 30 5xþ 5 ¼ 30 Combine 2xþ3x 5xþ 5
5 ¼ 30
5 Subtract 5 5x¼ 25 5 x 5 ¼ 25 5 Divide by 5 x¼ 5 Check: 2xþ 5 þ ...

Check: 3 ð2xþ 6 Þ¼ 30 3 ð 2  2 þ 6 Þ¼ 30 3  10 ¼ 30 30 ¼ 30 The procedure for solving equations in general is:  Step 1 Remove ...

PRACTICE Solve each of the following equations: 6xþ 4 ¼2xþ 12 x
10 ¼ 32
5x 9x
5 þ2x¼ 17 7x
3 ¼4x
27 10xþ 36 ¼6x 3(x
2)¼ 24 ...

SOLUTION xþ 15 2x
7 6x 3(xþ5) x 4 In solving word problems it is also necessary to represent two quantities using the same v ...

ANSWERS x, xþ 5 x, 50
x x, 5x x,^12 xorx,2x x, 2xþ 10 Word Problems Equations can be used to solve word problems in algebra. A ...

EXAMPLE A carpenter cuts a board 72 inches long into two pieces. One piece is twice as long as the other. Find the lengths of th ...

PRACTICE A stick 56 inches long is broken into two pieces so that one piece is 28 inches longer than the other piece. Find the ...

Solve the equation for x: 0 : 42  500 ¼x 210 ¼x (Be sure to change the percent to a decimal before multiplying.) EXAMPLE 15 is ...