Section 3

1. Solve for � x : 3 � +7=223 x +7=22 .  Answer : � =5 x =5 . 2. Find the value of � y if 2 � −5=112 y −5=11 .  Answer : � =8 y =8 . 3. Calculate the perimeter of a rectangle with length 1010 units and width 66 units.  Answer : Perimeter = 2×(10+6)=322×(10+6)=32 units. 4. Determine the value of � z in the equation 4 � −9=234 z −9=23 .  Answer : � =8 z =8 . 5. Solve the equation 2( � −3)=102( x −3)=10 .  Answer : � =8 x =8 . 6. Evaluate the expression: 53−2×45 3 −2×4 .  Answer : 53−2×4=125−8=1175 3 −2×4=125−8=117 . 7. Compute the area of a circle with a radius of 66 units (use � =3.14 π =3.14 ).  Answer : Area = � × � 2=3.14×62=113.04 π × r 2 =3.14×6 2 =113.04 square units. 8. Solve the inequality: 2 � +5>152 x +5>15 .  Answer : � >5 x >5 . 9. Find the slope of the line passing through points (−2,4)(−2,4) and (3,−1)(3,−1) .  Answer : Slope = −1−43−(−2)=−55=−1 3−(−2)−1−4 = 5−5 =−1 . 10. Solve for � y in the equation 3 � −7=83 y −7=8 .  Answer : � =5 y =5 . 11. Calculate the volume of a cube with side length 44 units.  Answer : Volume = 43=644 3 =64 cubic units. 12. Factorize the quadratic expression: � 2+6 � +9 x 2 +6 x +9 .  Answer : � 2+6 � +9=( � +3)2 x 2 +6 x +9=( x +3) 2 . 13. Solve the system of equations: {2 � +3 � =124 � − � =7 { 2 x +3 y =124 x − y =7  Answer : � =2, � =2 x =2, y =2 . 14. Determine the midpoint between points (−3,4)(−3,4) and (5,−2) (5,−2) .  Answer : Midpoint = (−3+52,4+(−2)2)=(1,1) ( 2−3+5 , 24+(−2) ) =(1,1) . 15. Find the value of � z in the equation 5( � +3)=405( z +3)=40 .  Answer : � =5 z =5 .