For problems #1-9 Solve each equation.
1) \(9x-13=2x+8\)
2) \(21x-5=-4x+25\)
3) \(2(3x-5)=3(2x+2)\)
4) \(-5(3x-10)=4(3x-1)\)
5) \(8(2x+1)-7=-6(4x+5)+11\)
6) \(5(5x-4)+3x=7(4x-2)-6\)
7) \(-\large{\frac{1}{6}}x-\large{\frac{2}{3}}=\large{\frac{1}{2}x+4}\)
8) \(\large\frac{5}{3}x-\frac{1}{6}=-\frac{5}{6}x+\frac{1}{4}\)
9) Last week you took \(4\) friends to a football game. On the way to the game, you stopped at the store and spent \(\$45\) dollars on snacks for the game. If you spent a total of \(\$230\), which included the \(5\) tickets and the cost of snacks, how much did each ticket cost? Set up a linear equation and solve it.
10)You are comparing the costs of two different monthly subscriptions. Option A has a subscription fee of \(\$15\) and is then \(\$15\) per month. Option B has a subscription fee of \(\$50\) but is only \(\$10\) per month. After how many months will Option B be the more cost effective option?
For problems #11-13 solve the equations for the indicated variable.
11) \(P=2l+2w\); for \(w\)
12) \(V=\frac{1}{3}\pi r^2h\); for \(r\)
13) \(S=B+\frac{1}{2}Pl\); for \(P\)
For problems #14-19 solve each equation for \(y\) in terms of \(x\).
14) \(5x-6y=24\)
15) \(-2x+\frac{1}{3}y=10\)
16) \(2xy=8+4x\)
17) \(6+15x=3xy\)
18) \(5y-2x=3xy+4\)
19) \(-4x-3xy=-9y-15\)
For problems #20-24 solve and graph each inequality.
20) \(2\left(4x-3\right)\ge 2x+18\)
21) \(3(7x-1)-9x>21\) or \(2x-4\ge4(x+5)\)
22) \(-4<\frac{4}{5}(x-3)<8\)
23) \(9\le-2x+7<17\)
24) \(6(2x-1)\ge4(3x+2)\)
Solution Bank
1) \(9x-13=2x+8\)
2) \(21x-5=-4x+25\)
3) \(2(3x-5)=3(2x+2)\)
4) \(-5(3x-10)=4(3x-1)\)
5) \(8(2x+1)-7=-6(4x+5)+11\)
6) \(5(5x-4)+3x=7(4x-2)-6\)
7) \(-\large{\frac{1}{6}}x-\large{\frac{2}{3}}=\large{\frac{1}{2}x+4}\)
8) \(\large\frac{5}{3}x-\frac{1}{6}=-\frac{5}{6}x+\frac{1}{4}\)
9) Last week you took \(4\) friends to a football game. On the way to the game, you stopped at the store and spent \(\$45\) dollars on snacks for the game. If you spent a total of \(\$230\), which included the \(5\) tickets and the cost of snacks, how much did each ticket cost? Set up a linear equation and solve it.
10)You are comparing the costs of two different monthly subscriptions. Option A has a subscription fee of \(\$15\) and is then \(\$15\) per month. Option B has a subscription fee of \(\$50\) but is only \(\$10\) per month. After how many months will Option B be the more cost effective option?
For problems #11-13 solve the equations for the indicated variable.
11) \(P=2l+2w\); for \(w\)
12) \(V=\frac{1}{3}\pi r^2h\); for \(r\)
13) \(S=B+\frac{1}{2}Pl\); for \(P\)
For problems #14-19 solve each equation for \(y\) in terms of \(x\).
14) \(5x-6y=24\)
15) \(-2x+\frac{1}{3}y=10\)
16) \(2xy=8+4x\)
17) \(6+15x=3xy\)
18) \(5y-2x=3xy+4\)
19) \(-4x-3xy=-9y-15\)
For problems #20-24 solve and graph each inequality.
20) \(2\left(4x-3\right)\ge 2x+18\)
21) \(3(7x-1)-9x>21\) or \(2x-4\ge4(x+5)\)
22) \(-4<\frac{4}{5}(x-3)<8\)
23) \(9\le-2x+7<17\)
24) \(6(2x-1)\ge4(3x+2)\)
Solution Bank