Pre-Calc

Pre-Calc

1. Absolute value equations

   • |y| = a
     • y = a
     • y=-a
   • Inequalities
     • |y| <= a
       • -a<=y<=a
         • |5 - 2x| &lt;= 9 -9&lt;= 5-2x&lt;= 9 -9 (-5) &lt;= 5(-5)-2x&lt;= 9 (-5)&nbsp;&nbsp; (solve for x.&nbsp; Subtract 5) -14&lt;= -2x&lt;= 4 -14/-2 =&gt; -2x/-2 =&gt; 4/-2&nbsp;&nbsp; (divide by -2. ) &nbsp; NOTE:Switch inequalities when dividing by negative) 7 =&gt; x =&gt; -2&nbsp;&nbsp; or&nbsp;&nbsp; -2&lt;=x&lt;=7
     • |y| < a
       • y < a
       • y > -a

2. Polynomials

   • Add and Subtract
     • (ax^2 +x - 7) + (bx^2 -3x +9)
       • ax^2 + bx^2 +x - 3x - 7 + 9
         • (a+b)x^2 -2x +2
     • (ax^2 +x - 7) - (bx^2 -3x +9)
       • ax^2 - bx^2 + x +3x -7 -9
         • (a-b)x^2 +4x - 16

3. Rational Expressions

   • Add and Subtract
     • 5/x-1 + 4/x-2
       • 5(x-2)/(x-1)(x-2) + 4(x-1)/(x-2)(x-1)
         • (5x-10)/(x-1)(x-2) + (4x-4)/(x-2)(x-1)
           • (9x-14)/(x-1)(x-2)