Chapter 1

Write each of the following as a mathematical expression, and simplify. Add \(8 t+5\) to \(10 t-8\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(-2 y^{2}+3 a^{2}\)

Write a numerical expression for each phrase, and simplify the expression. The sum of -5 and 12 and 6

Write each of the following as a mathematical expression, and simplify. Subtract \(x-7\) from \(5 x+1\)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(5 x^{2}-4 y^{2}\)

Write a numerical expression for each phrase, and simplify the expression. The sum of -3 and 5 and -12

Write each of the following as a mathematical expression, and simplify. Subtract \(3 x-5\) from \(2 x-3\).

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\frac{5 y^{2}+4}{x}\)

Write a numerical expression for each phrase, and simplify the expression. 14 added to the sum of -19 and -4

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. Five times a number, added to the sum of the number and three

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\frac{11-3 a^{2}}{y}\)

Write a numerical expression for each phrase, and simplify the expression. -2 added to the sum of -18 and 11

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. Six times a number, added to the sum of the number and six

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. A number multiplied by \(-7,\) subtracted from the sum of 13 and six times the number

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\frac{x y+8 a}{x-6}\)

Write a numerical expression for each phrase, and simplify the expression. The sum of -7 and -13 , increased by 14

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. A number multiplied by \(5,\) subtracted from the sum of 14 and eight times the number

Write a numerical expression for each phrase, and simplify the expression. The product of -9 and \(2,\) added to 9

Write a numerical expression for each phrase, and simplify the expression. 1.85 more than the sum of -1.25 and -4.75

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. Nine times a number added to \(6,\) subtracted from triple the sum of 12 and 8 times the number

Write a numerical expression for each phrase, and simplify the expression. The difference of 4 and -8

Twice the product of -1 and \(6,\) subtracted from -4

Write a numerical expression for each phrase, and simplify the expression. The difference of 7 and -14

A manufacturer has fixed costs of \(\$ 1000\) to produce gizmos. Each gizmo costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(y\) gadgets.

Write a numerical expression for each phrase, and simplify the expression. 8 less than -2

A manufacturer has fixed costs of \(\$ 1000\) to produce gizmos. Each gizmo costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the total cost to make \(x\) gizmos and \(y\) gadgets.

Write a numerical expression for each phrase, and simplify the expression. 9 less than -13

Write a numerical expression for each phrase, and simplify the expression. The product of 12 and the difference of 9 and -8

Write a numerical expression for each phrase, and simplify the expression. The sum of 12 and \(-7,\) decreased by 14

Write a numerical expression for each phrase, and simplify the expression. 12 less than the difference of 8 and -5

Write a numerical expression for each phrase, and simplify the expression. 19 less than the difference of 9 and -2

Write a numerical expression for each phrase, and simplify the expression. The sum of 15 and \(-3,\) divided by the product of 4 and -3

Write a numerical expression for each phrase, and simplify the expression. The sum of -18 and \(-6,\) divided by the product of 2 and -4

Write a numerical expression for each phrase, and simplify the expression. Two-thirds of the difference of 8 and -1

The table gives scores (above or below par-that is, above or below the score "standard") for selected golfers during the 2017 Blue Bay LPGA Tournament. Write a signed number that represents the total score (above or below par) for the four rounds for each golfer.

Write a numerical expression for each phrase, and simplify the expression. Three-fourths of the sum of -8 and 12

Solve each problem. Based on 2020 population projections, Illinois will probably lose 2 seats in the U.S. House of Representatives, Minnesota will lose 1 seat, and New York will lose 1 . Write a signed number that represents the total number of seats these three states are projected to lose. (Data from Election Data Services.)

Write a numerical expression for each phrase, and simplify the expression. \(30 \%\) of the product of -8 and 5

Solve each problem. Both Alabama and Ohio are projected to lose 1 seat in the U.S. House of Representatives in 2020 . The states projected to gain the most seats are Texas with 4 and Florida with \(2 .\) Write a signed number that represents the algebraic sum of these changes. (Data from Election Data Services.)

Write a numerical expression for each phrase, and simplify the expression. The sum of \(\frac{1}{2}\) and \(\frac{5}{8},\) times the difference of \(\frac{3}{5}\) and \(\frac{1}{3}\)

Solve each problem. The surface, or rim, of a canyon is at altitude \(0 .\) On a hike down into the canyon, a party of hikers stops for a rest at \(130 \mathrm{~m}\) below the surface. The hikers then descend another \(54 \mathrm{~m}\). Write the new altitude as a signed number.

Write a numerical expression for each phrase, and simplify the expression. The sum of \(\frac{3}{4}\) and \(\frac{1}{2},\) times the difference of \(\frac{2}{3}\) and \(\frac{1}{6}\)

Solve each problem. A pilot announces to the passengers that the current altitude of their plane is \(34,000 \mathrm{ft}\). Because of turbulence, the pilot is forced to descend \(2100 \mathrm{ft}\). Write the new altitude as a signed number.

Write a numerical expression for each phrase, and simplify the expression. The product of \(-\frac{1}{2}\) and \(\frac{3}{4},\) divided by \(-\frac{2}{3}\)

Solve each problem. The lowest temperature ever recorded in Arkansas was \(-29^{\circ} \mathrm{F}\). The highest temperature ever recorded there was \(149^{\circ} \mathrm{F}\) more than the lowest. What was this highest temperature? (Data from National Climatic Data Center.)

Write a numerical expression for each phrase, and simplify the expression. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)

Solve each problem. The lowest temperature ever recorded in Illinois was \(-36^{\circ} \mathrm{F}\) on January \(5,1999 .\) The lowest temperature ever recorded in Utah was on February \(1,1985,\) and was \(33^{\circ} \mathrm{F}\) lower than Illinois's record low. What is the record low temperature for Utah? (Data from National Climatic Data Center.)

Solve each problem. Nadine enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were $$ \begin{array}{lllll} -19, & 28, & -5, & \text { and } & 13 . \end{array} $$ What was her final score for the four turns?

Solve each problem. In 2005, Americans saved \(-0.5 \%\) of their after-tax incomes. In September 2017 , they saved \(3.1 \%\). (Data from U.S. Bureau of Economic Analysis.) (a) Express the difference between these amounts as a positive number. (b) How could Americans have a negative personal savings rate in \(2005 ?\)

Solve each problem. In \(2000,\) the U.S. federal budget had a surplus of \(\$ 236\) billion. In \(2016,\) the federal budget had a deficit of \(\$ 616\) billion. Express the difference between these amounts as a positive number. (Data from U.S. Office of Management and Budget.)