Page 471 - Algebra 1

When solving an equation, the equality symbol never changes. Each transformation results in an equation equivalent to the previous equation. Multiplying an inequality by a positive value is similar to solving an equation because the symbol of inequality does not change, regardless of the operations required to solve the statement. However, when multiplying an inequality by a negative value, the order of the inequality does change.
5 > 3, so 5(-2) < 3(-2) because -10 < -6. 8 < 12, so 8(-4) > 12(-4) because -32 > -48.
Multiplying by a Negative Number
-x _
Math Language
A transformation is a change in a statement that is the result of an operation performed on an equality or inequality.
Multiplication Property of Inequality for c < 0
For every real number a and b, and c < 0: If a>b,thenac<bc.
If a<b,thenac>bc.
This property is also true for ≥ and ≤.
Example
2
Solve, graph, and check the solution for the inequality 5
< 5.
SOLUTION
Solve the inequality.
Hint
When the coefficient of a variable of an inequality is a fraction, multiply by the reciprocal to solve.
_
-x <5
5 _
(-5)-x >5(-5) 5
MultiplicationPropertyofInequalityforc<0 Simplify.
x > -25
Graph the solution on a number line.
Check
-25 -15 -5 5
Check the endpoint. Check the direction of the inequality. __
-x 5 -x 5 -(-25) 5 -(-20) 5
_5 _5 55
__
25 5 20 5
55
5=5 ✓ 4<5 ✓
Both statements are true, so the solution is correct.
456 Saxon Algebra 1