IM1: Solving Equations and Inequalities Review

Solving Equations

100

Solve the equation.

`5x-11=12`

`x=4.6`

200

Solve the equation. 

`-2x-(-4)=8`

`x=-2`

300

Solve the equation. 

`15=1/2x+18`

`x=-6`

400

Solve the equation. 

`5x-7=-3x+9`

`x=2`

500

Solve the equation. 

`4(x-5)=3x+7`

`x=27`

Solving Inequalities

100

Solve the inequality. 

`2x-9<=-11`

`x<=-1`

200

Solve the inequality. 

`4x+9<7x+9`

`x>0`

300

Solve the inequality. 

`-5x+11> -1`

`x<2.4`

400

Solve the inequality. 

`3(x-2) + x <4x+11`

Infinite Solutions

500

Solve the inequality. 

`21<-1/3x+9`

`x<-36`

Word Problems

100

Five times a number decreased by 7 is 25.

`5x-7=25`

200

Half the difference of a number and 8 is 17. 

`1/2(x-8)=17 or (x-8)/2=17`

300

The quotient of a number and 6 decreased by 9 is more than 8. 

`x/6-9>8`

400

The product of a number and 3 increased by 1 is no less than 4. 

`3x+1>=4`

500

Five times the sum of a number and 8 is at most 15. 

`5(x+8)<=15`

Fractions

100

Solve. 

`3/4x>12`

`x>16`

200

Solve. 

`-x/5-4=-9`

`x=25`

300

Solve. 

`-2/9(18x-27)=-2`

`x=2`

400

Solve. 

`-4<=(x-7)/3`

`x>=-5`

500

Solve. 

`1/4(12-4x)=3(1-2x)+5x`

Infinite Solutions

Complex Inequalities

100

Solve the inequality.

`-5<2x+9<=11`

`-7<x<=1`

200

Solve the inequality. 

`3x-1<-10 or 1/2x-5>11`

`x<-3 or x>32`

300

Solve the inequality.

`-4x-7>3 or 5x + 9>=20`

`x<-2.5 or x>=2.2`

400

Solve the inequality.

`-9<=7x+5<=26`

`-2<=x<=3`

500

Solve the inequality.

`1<2/3x+7<19`

`-9<x<18`