1. Equations & Inequalities

Solve each problem. If 120 L of an acid solution is 75% acid, how much pure acid is there in the mixture?

Solve each equation for x. 3x=(2x-1)(m+4)

Solve each equation. |x + 1 | = |1 -3x|

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

Solve each equation. 0.08x+0.06(x+12) = 7.72

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |4x - 3| = |4x - 5|

Solve each problem. If a train travels at 80 mph for 15 min, what is the distance traveled?

Find all values of x satisfying the given conditions. y₁ = (2x - 1)/(x² + 2x - 8), y₂ = 2/(x + 4), y₃ = 1/(x - 2), and y₁ + y₂ = y₃.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 1/(x - 1) + 5 = 11/(x - 1)

Solve and check each linear equation. 4x + 9 = 33