Chapter 2

Use both the addition and multiplication properties of inequality to solve each inequality and graph the solution set on a number line. $$\frac{x}{4}-3 \geq 1$$

Determine whether each statement “makes sense” or “does not make sense” and explain your reasoning. When I use the addition and multiplication properties to solve \(2 x+5=17,\) I undo the operations in the opposite order in which they are performed.

Solve equation. Use words or set notation to identify equations that have no solution, or equations that are true for all real numbers. \(0.04(x-2)=0.02(6 x-3)-0.02\)

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

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 .

Contain small figures ( \(\square, \triangle\) and \(\$$ ) that represent nonzero real numbers. Use properties of equality to isolate \)x\( on one side of the equation and the small figures on the other side. \)\frac{x}{\square}+\Delta=\$$

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

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

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

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

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

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

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

In Exercises \(79-82,\) 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 \(y=x+7\)

Solve each inequality. $$x+3

It is possible to have a circle whose circumference is numerically equal to its area.

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

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 one-third of a number is added to one-fifth of the number, the sum is \(16 .\) What is the number?

In Exercises \(79-82,\) determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. 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 \(C\).

Solve each inequality. $$x+4

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)

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?

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

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 )

When 3 is subtracted from three-fourths of a number, the result is equal to one-half of the number. What is the number?

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

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

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

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?

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

Suppose you know the cost for building a rectangular deck measuring 8 feet by 10 feet. If you decide to increase the dimensions to 12 feet by 15 feet, by how many times will the cost increase?

Will help you prepare for the material covered in the next section. Multiply and simplify: \(\quad 5 \cdot \frac{x}{5}\)

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

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?

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

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?

Will help you prepare for the material covered in the next section. Divide and simplify: \(\frac{-7 y}{-7}\)

Evaluate: \((-10)^{2}\)

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?

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

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

Will help you prepare for the material covered in the next section. Is 4 a solution of \(3 x-14=-2 x+6 ?\)

Evaluate: \(-10^{2}\)

Solve each inequality. $$6 x-3 \leq 3(x-1)$$

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?

Evaluate \(x^{3}-4 x\) for \(x=-1\).

Use properties of inequality to rewrite each inequality so that \(x\) is isolated on one side. $$3 x+a>b$$

Exercises \(91-93\) will help you prepare for the material covered in the next section. Simplify: \(13-3(x+2)\)