(1) 4/3r – 3 < r + 2/3 - 1/3r the first thing you want to do is combine the "r's" on the right side. that would be r - 1/3r that gives you 2/3r on the right side. now your equation should look like this: 4/3r - 3 < 2/3r + 2/3 the next thing you want to do is move your "2/3r" to the left side of the inequality sign. to move it you would have to subtract it. 4/3r - 3 - 2/3r < 2/3r + 2/3- 2/3r now your equation should look like this: 2/3r - 3 < 2/3 move your -3 over to the right side by adding it 2/3r - 3 + 3 < 2/3 + 3 your equation should look like this: 2/3r < 3 2/3 now to solve for r you will have to multiply 2/3 by its reciprocal. if you don't know what that is, it is simply the fraction inversed. 2/3 reciprocal is 3/2. multiplying on 3 2/3 by 3/2 will be easier if you turn it into an improper fraction. so 3 2/3 as an improper fraction would be 11/3 your equation should look like this: 2/3r < 11/3 (3/2) 2/3r < 11/3 (3/2) when you multiply 3/2 by 2/3 they give you 1. as you know you don't write 1 in front of a variable. so your equation should look like this r < 33/6 you could turn 33/6 into a mixed number which would be 5 3/6 or 5 1/2 so the answer is r < 5 1/2 (2) -2m_< 5-m+1 combine your like terms on the right side -2m_< 6-m move your -m to the left side (add it) -m_< 6 now you're going to divide both sides by negative 1 to fully isolate m. but when you divide by a negative you have to reverse the sign of the inequality so your answer is: m >_ -6

think you got the hang now?

-2(0.5-4s) >_ -3(4-3.5s)

multiply what’s outside of parentheses by what’s inside of parentheses on both sides

so it becomes

-1+8s >_ -12 + 10.5s

whenever you multiply or divide two negatives, they become positive

move your s over to the left side

subtract it

-1 – 2.5s >_ -12

move your -1 to the right side

-2.5s >_ -11

divide both sides by -2.5

don’t forget to reverse your inequality sign

s <_ 4.4

Simply bring the terms with the unknowns ie r, m, s, etc, to one side of the equation and the numbers to the other side.

4) 1/2 n – 1/8 >_ 3/4 + 5/6 n

1/2 n – 5/6 n >_ 3/4 + 1/8

-1/3 n >_ 7/8

-n >_ 21/8

21/8 >_ n

n <_ 21/8 P.s: Be careful when dividing throughout by a negative number for inequalities. Greater than becomes smaller than and vice versa.