7. Self-Test
Answers to the questions are available at the end of the book.
For problems 1 and 2, write the algebraic expression.
- a. Twenty-five less than three times a number.
b. A number increased by eighteen. - a. The difference between twice a number and six.
b. A number divided by three.
For problems 3 and 4, simplify the expressions, then evaluate for the given value of the variables in the brackets.
- a. [latex]-3x^2 + 2x + 2x^2 - 8x + 10[/latex] [latex](x = -3)[/latex]
b. [latex]5(2x - 3y) - 2(3x - 2y) + 7[/latex] [latex](x = 2 and y = 1)[/latex] - a. [latex](x + 3)^2 - (x + 2)(x - 2)[/latex] [latex](x = 3)[/latex]
b. [latex](2x + 5)^2 - (3x - 1 )^2[/latex] [latex](x = 1)[/latex]
For problems 5 and 6, write the algebraic equation and solve.
- a. Nine less than twice a number is twenty-one.
b. Twenty-two is five times a number less than three. - a. Four times eight is sixteen times a number.
b. Thirty is a product of six and a number.
For problems 7 and 8, solve for the unknown variable, x, using the principles of equality.
- a. [latex]24-5x = 4[/latex]
b. [latex]\displaystyle{\frac{x}{3} - 2 = 4}[/latex] - a. [latex]8 + 2x = 4 - 5x[/latex]
b. [latex]3(3x - 3) = 33[/latex]
Unless otherwise indicated, this chapter is an adaptation of the eTextbook Foundations of Mathematics (3rd ed.) by Thambyrajah Kugathasan, published by Vretta-Lyryx Inc., with permission. Adaptations include supplementing existing material and reordering chapters.
