Chapter 1

Simplify each expression, if possible. a. \(2(7 x) 5\) b. \(2(7 x+5)\)

Find \(\frac{1}{2}+\frac{1}{4}+\frac{1}{3}\). Answer in decimal form.

What numbers are a distance of 6 away from \(-11\) on a number line?

Simplify each expression, if possible. a. \(-3(-4 a)(-2)\) b. \(-3(-4 a)-2\)

Which integers have an absolute value equal to \(45 ?\)

Fill in the blank with \(>\) or \(<: 0.3 \quad \frac{1}{3}\)

Recall that the perimeter of a figure is equal to the sum of the lengths of its sides. First Aid. Each side of the red cross has length \(x\) inches. Write an algebraic expression that represents the perimeter of the cross.

If the product of five numbers is negative, how many of them could be negative? Explain.

Using each of the numbers \(2,3,\) and 4 only once, what is the greatest value that the following expression can have?

Suppose \(a\) is a positive number and \(b\) is a negative number. Determine whether the given expression is positive or negative. a. \(-a(-b)\) b. \(\frac{-a}{b}\) c. \(\frac{-a}{a}\) d. \(\frac{1}{b}\)

Insert a pair of parentheses into \(4 \cdot 3^{2}-4 \cdot 2\) so that it has a value of 40

Explain why the distributive property applies to \(2(3+x)\) but not to \(2(3 x)\)

Translate the set of instructions to an expression and then evaluate it. Subtract the sum of \(-9\) and 8 from the product of the cube of \(-3\) and the opposite of 4

Explain each error. Then give the correct answer. a. \(9(4 b-2)=36 b-2\) b. \(\quad 3(2 x)=6 \cdot 3 x=18 x\) c. \(-(23 c+2)=-23 c+2\) d. \((5 n+1) 2=5 n+2\)

Translate the set of instructions to an expression and then evaluate it. Increase the square of the reciprocal of \(-2\) by the difference of \(-0.25\) and \(-1\)

Evaluate each expression for \(x=-3\) and \(y=-5\) $$ \frac{x-y^{2}}{2 y-1+x} $$

Evaluate each expression for \(x=-3\) and \(y=-5\) $$ \frac{2 y+1}{x}-x $$

Simplify. $$ 2\\{-2[x+4(2 x+1)]-5[x+2(3 x+4)]\\}+106 x $$