Chapter 2

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(1-\frac{x}{2}>4\)

Make Sense? Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The model \(P=18 n+765\) describes the price of a Westie puppy, \(P, n\) years after \(1940,\) so I have to solve a linear equation to determine the puppy's price in 2009 .

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\text { If } A=l w, \text { then } w=\frac{l}{A}$$

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. \(1-\frac{x}{2}<5\)

Write an cquation with a negative solution that can be solved by adding 100 to both sides.

Solve each inequality. \(4 x-4<4(x-5)\)

If \(\frac{x}{5}-2=\frac{x}{3},\) evaluate \(x^{2}-x\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I find that my answers involving \(\pi\) can vary slightly depending on whether I round \(\pi\) mid-calculation or use the \(\pi\) key on my calculator and then round at the very end.

Use a calculator to solve each equation. $$x-7.0463=-9.2714$$

Solve each inequality. \(3 x-5<3(x-2)\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Solving \(x-y=-7\) for \(y\) gives \(y=x+7\)

If \(\frac{3 x}{2}+\frac{3 x}{4}=\frac{x}{4}-4,\) evaluate \(x^{2}-x\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The solution of \(6 x=0\) is not a natural number.

Use a calculator to solve each equation. $$6.9825=4.2296+y$$

Solve each inequality. \(x+3

In psychology, an intelligence quotient, \(Q,\) also called IQ, is measured by the formula $$Q=\frac{100 M}{C}$$ where \(M=\) mental age and \(C=\) chronological age. Solve the formula for \(C .\)

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. When one-third of a number is added to one-fifth of the number, the sum is \(16 .\) What is the number?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. When the measure of a given angle is added to three times the measure of its complement, the sum equals the sum of the measures of the complement and supplement of the angle.

Write as an algebraic expression in which \(x\) represents the number: the quotient of 9 and a number, decreased by 4 times the number. (Section 1.1, Example 3)

Solve each inequality. \(x+4

Solve and check: \(5 x+20=8 x-16\)

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. When two-fifths of a number is added to one-fourth of the number, the sum is 13. What is the number?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The complement of an angle that measures less than \(90^{\circ}\) is an angle that measures more than \(90^{\circ} .\)

Simplify: \(-16-8 \div 4 \cdot(-2) .\) (Section \(1.8,\) Example 4 )

Solve each inequality. \(7 x \leq 7(x-2)\)

Solve and check: \(5(2 y-3)-1=4(6+2 y)\)

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. When 3 is subtracted from three-fourths of a number, the result is equal to one-half of the number. What is the number?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Two complementary angles can be equal in measure.

Simplify: \(3[7 x-2(5 x-1)] .\) (Section \(1.8,\) Example 11 )

Solve each inequality. \(3 x+1 \leq 3(x-2)\)

Solve each equation .Use a calculator to help with the arithmetic. Check your solution using the calculator. 6\. \(3.7 x-19.46=-9.988\)

Simplify: \(x-0.3 x\).

Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. When 30 is subtracted from seven-eighths of a number, the result is equal to one-half of the number. What is the number?

Multiply and simplify: \(\quad 5 \cdot \frac{x}{5}\).

Solve each inequality. \(2(x+3)>2 x+1\)

Solve each equation .Use a calculator to help with the arithmetic. Check your solution using the calculator. \(-72.8 y-14.6=-455.43-4.98 y\)

Let x represent the number and write the phrase as an algebraic expression. The quotient of 13 and a number, decreased by 7 times the number

In Massachusetts, speeding fines are determined by the formula $$F=10(x-65)+50$$ where \(F\) is the cost, in dollars, of the fine if a person is caught driving \(x\) miles per hour. Use this formula to solve. If a fine comes to \(\$ 250,\) how fast was that person driving?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A rectangular swimming pool measures 14 feet by 30 feet. The pool is surrounded on all four sides by a path that is 3 feet wide. If the cost to resurface the path is \(\$ 2\) per square foot, what is the total cost of resurfacing the path?

Divide and simplify: \(\frac{-7 y}{-7}\).

Solve each inequality. \(5(x+4)>5 x+10\)

Solve each equation .Use a calculator to help with the arithmetic. Check your solution using the calculator. Evaluate: \((-10)^{2} .\)

Let x represent the number and write the phrase as an algebraic expression. Eight times the sum of a number and 14

In Massachusetts, speeding fines are determined by the formula $$F=10(x-65)+50$$ where \(F\) is the cost, in dollars, of the fine if a person is caught driving \(x\) miles per hour. Use this formula to solve. If a fine comes to \(\$ 400,\) how fast was that person driving?

What happens to the volume of a sphere if its radius is doubled?

Is 4 a solution of \(3 x-14=-2 x+6 ?\)

Solve each inequality. \(5 x-4 \leq 4(x-1)\)

Solve each equation .Use a calculator to help with the arithmetic. Check your solution using the calculator. Evaluate: \(-10^{2}\).

Let x represent the number and write the phrase as an algebraic expression. Nine times the difference of a number and 5

A scale model of a car is constructed so that its length, width, and height are each \(\frac{1}{10}\) the length, width, and height of the actual car. By how many times does the volume of the car exceed its scale model?