Algebra

Linear Inequalities

Linear Inequalities - Problem Solving

         

If x+y=7 x+y = 7 and 4x19, 4 \leq x \leq 19, what is the range of y?y?

If the inequality a2(x+1)>576x+24aa^2(x+1)>576 x+24a holds for all real numbers x,x, what is the constant a?a?

Let x>1413x>\frac{14}{13} be the solution to the inequality bx(a+b)<0,bx-(a+b)<0, where aa and bb are constants. Then what is the solution to the inequality ax+2a+b<0?ax+2a+b<0?

A factory produces two products AA and BB using raw materials pp and qq. It uses 33 units of pp and 11 unit of qq to produce one unit of AA. It uses 11 unit of pp and 22 units of qq to produce one unit of BB. The maximum daily supplies are 3030 units of pp and 2020 units of q.q. If the profit per unit of AA is $3\$3 and the profit per unit of BB is $2\$2, what is the maximum total daily profit (in dollars)?

Real numbers xx and yy satisfy 3<x<1 -3 < x < 1 and 1<y<5 -1 < y < 5. What is the range of xy? x - y ?

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