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Section 1

The Addition Property of Equality

Decide whether each of the following is an expression or an equation. If it is an expression, simplify it. If it is an equation, solve it.(b) $-6 y+12+7 y-5$(a) $5 x+8-4 x+7$(c) $5 x+8-4 x=7$(d) $-6 y+12+7 y=-5$

Which pairs of equations are equivalent equations?A. $x+2=6$ and $x=4$B. $10-x=5$ and $x=-5$C. $x+3=9$ and $x=6$D. $4+x=8$ and $x=-4$

Which of the following are not linear equations in one variable?$$\begin{array}{llll}{\text { A. } x^{2}-5 x+6=0} & {\text { B. } x^{3}=x} & {\text { C. } 3 x-4=0} & {\text { D. } 7 x-6 x=3+9 x}\end{array}$$

Explain how to check a solution of an equation.

Solve each equation, and check your solution.$$x-3=9$$

Solve each equation, and check your solution.$$x-9=8$$

Solve each equation, and check your solution.$$x-12=19$$

Solve each equation, and check your solution.$$x-18=22$$

Solve each equation, and check your solution.$$x-6=-9$$

Solve each equation, and check your solution.$$x-5=-7$$

Solve each equation, and check your solution.$$r+8=12$$

Solve each equation, and check your solution.$$x+7=11$$

Solve each equation, and check your solution.$$x+28=19$$

Solve each equation, and check your solution.$$x+47=26$$

Solve each equation, and check your solution.$$x+\frac{1}{4}=-\frac{1}{2}$$

Solve each equation, and check your solution.$$x+\frac{2}{3}=-\frac{1}{6}$$

Solve each equation, and check your solution.$$7+r=-3$$

Solve each equation, and check your solution.$$8+k=-4$$

Solve each equation, and check your solution.$$2=p+15$$

Solve each equation, and check your solution.$$5=z+19$$

Solve each equation, and check your solution.$$-4=x-14$$

Solve each equation, and check your solution.$$-7=x-22$$

Solve each equation, and check your solution.$$-\frac{1}{3}=x-\frac{3}{5}$$

Solve each equation, and check your solution.$$-\frac{1}{4}=x-\frac{2}{3}$$

Solve each equation, and check your solution.$$x-8.4=-2.1$$

Solve each equation, and check your solution.$$x-15.5=-5.1$$

Solve each equation, and check your solution.$$t+12.3=-4.6$$

Solve each equation, and check your solution.$$x+21.5=-13.4$$

Solve each equation, and check your solution.$$3 x=2 x+7$$

Solve each equation, and check your solution.$$5 x=4 x+9$$

Solve each equation, and check your solution.$$10 x+4=9 x$$

Solve each equation, and check your solution.$$8 t+5=7 t$$

Solve each equation, and check your solution.$$3 x+7=2 x+4$$

Solve each equation, and check your solution.$$9 x+1=8 x+4$$

Solve each equation, and check your solution.$$8 t+6=7 t+6$$

Solve each equation, and check your solution.$$13 t+9=12 t+9$$

Solve each equation, and check your solution.$$-4 x+7=-5 x+9$$

Solve each equation, and check your solution.$$-6 x+3=-7 x+10$$

Solve each equation, and check your solution.$$\frac{2}{5} w-6=\frac{7}{5} w$$

Solve each equation, and check your solution.$$\frac{2}{7} z-2=\frac{9}{7} z$$

Solve each equation, and check your solution.$$5.6 x+2=4.6 x$$

Solve each equation, and check your solution.$$9.1 x+5=8.1 x$$

Solve each equation, and check your solution.$$1.4 x-3=0.4 x$$

Solve each equation, and check your solution.$$1.9 t-6=0.9 t$$

Solve each equation, and check your solution.$$5 p=4 p$$

Solve each equation, and check your solution.$$8 z=7 z$$

Solve each equation, and check your solution.$$1.2 y-4=0.2 y-4$$

Solve each equation, and check your solution.$$7.7 r-6=6.7 r-6$$

Solve each equation, and check your solution.$$\frac{1}{2} x+5=-\frac{1}{2} x$$

Solve each equation, and check your solution.$$\frac{1}{5} x+7=-\frac{4}{5} x$$

Solve each equation, and check your solution.$$3 x+7-2 x=0$$

Solve each equation, and check your solution.$$5 x+4-4 x=0$$

Solve each equation, and check your solution.$$5 t+3+2 t-6 t=4+12$$

Solve each equation, and check your solution.$$4 x+3 x-6-6 x=10+3$$

Solve each equation, and check your solution.$$6 x+5+7 x+3=12 x+4$$

Solve each equation, and check your solution.$$4 x-3-8 x+1=-5 x+9$$

Solve each equation, and check your solution.$$5.2 q-4.6-7.1 q=-0.9 q-4.6$$

Solve each equation, and check your solution.$$-4.0 x+2.7-1.6 x=-4.6 x+2.7$$

Solve each equation, and check your solution.$$\frac{5}{7} x+\frac{1}{3}=\frac{2}{5}-\frac{2}{7} x+\frac{2}{5}$$

Solve each equation, and check your solution.$$\frac{6}{7} s-\frac{3}{4}=\frac{4}{5}-\frac{1}{7} s+\frac{1}{6}$$

Solve each equation, and check your solution.$$(5 y+6)-(3+4 y)=10$$

Solve each equation, and check your solution.$$(8 r-3)-(7 r+1)=-6$$

Solve each equation, and check your solution.$$2(p+5)-(9+p)=-3$$

Solve each equation, and check your solution.$$4(k-6)-(3 k+2)=-5$$

Solve each equation, and check your solution.$$-6(2 b+1)+(13 b-7)=0$$

Solve each equation, and check your solution.$$-5(3 w-3)+(1+16 w)=0$$

Solve each equation, and check your solution.$$10(-2 x+1)=-19(x+1)$$

Solve each equation, and check your solution.$$2(2-3 r)=-5(r-3)$$

Solve each equation, and check your solution.$$-2(8 p+2)-3(2-7 p)-2(4+2 p)=0$$

Solve each equation, and check your solution.$$-5(1-2 z)+4(3-z)-7(3+z)=0$$

Solve each equation, and check your solution.$$4(7 x-1)+3(2-5 x)-4(3 x+5)=-6$$

Solve each equation, and check your solution.$$9(2 m-3)-4(5+3 m)-5(4+m)=-3$$

Write an equation that requires the use of the addition property of equality, in which 6 must be added to each side to solve the equation and the solution isa negative number.

Write an equation that requires the use of the addition property of equality, in which $\frac{1}{2}$ must be subtracted from each side and the solution is a positive number.

Write an equation using the information given in the problem. Use x as the variable. Then solve the equation.Three times a number is 17 more than twice the number. Find the number.

Write an equation using the information given in the problem. Use x as the variable. Then solve the equation.One added to three times a number is three less than four times the number. Find the number.

Write an equation using the information given in the problem. Use x as the variable. Then solve the equation.If six times a number is subtracted from seven times the number, the result is $-9 .$ Find the number.

Write an equation using the information given in the problem. Use x as the variable. Then solve the equation.If five times a number is added to three times the number, the result is the sum of seven times the number and $9 .$ Find the number.

Simplify each expression.$$\frac{2}{3}\left(\frac{3}{2}\right)$$

Simplify each expression.$$\frac{5}{6}\left(\frac{6}{5}\right)$$

Simplify each expression.$$-\frac{5}{4}\left(-\frac{4}{5} x\right)$$

Simplify each expression.$$-\frac{9}{7}\left(-\frac{7}{9} x\right)$$

Simplify each expression.$$9\left(\frac{r}{9}\right)$$

Simplify each expression.$$6\left(\frac{t}{6}\right)$$