1.4E: Exercises
- Page ID
- 108489
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Practice Makes Perfect
In the following exercises, determine whether the given value is a solution to the equation.
- Is \(y=\frac{5}{3}\) a solution of \(6 y+10=12 y ?\)
- Is \(u=-\frac{1}{2}\) a solution of \(8 u-1=6 u ?\)
- Is \(v=-\frac{1}{3}\) a solution of \(9 v-2=3 v ?\)
- Is \(v=\frac{1}{3}\) a solution of \(9 v-2=3 v ?\)
- Answer
-
- Yes
- No
- No
- Yes
In the following exercises, solve each equation using the Subtraction and Addition Properties of Equality.
- \(x+24=35\)
- \(y+45=-66\)
- \(b+\frac{1}{4}=\frac{3}{4}\)
- \(p+2.4=-9.3\)
- \(a-45=76\)
- \(m-18=-200\)
- \(x-\frac{1}{3}=2\)
- \(y-3.8=10\)
- \(x-165=-420\)
- \(z+0.52=-8.5\)
- \(q+\frac{3}{4}=\frac{1}{2}\)
- \(p-\frac{2}{5}=\frac{2}{3}\)
- \(c+31-10=46\)
- \(9 x+5-8 x+14=20\)
- \(-6 x-11+7 x-5=-16\)
- Answer
-
- x = 11
- y = -111
- \(b = \frac{1}{2}\)
- p = -11.7
- a = 121
- m = -182
- \(x=\frac{7}{3}\)
- y = 13.8
- \(x=-255\)
- \(z=-9.02\)
- \(q = -\frac{1}{4}\)
- \(p=\frac{16}{15}\)
- c = 25
- x = 1
- x = 0
In the following exercises, solve each equation using the Division and Multiplication Properties of Equality.
- \(8x=56\)
- \(-5 c=55\)
- \(-809=15 y\)
- \(-37 p=-541\)
- \(0.25 z=3.25\)
- \(-13x=0\)
- \(\frac{x}{4} = 35\)
- \(-20=\frac{q}{-5}\)
- \(\frac{y}{9}=-16\)
- \(\frac{m}{-12}=45\)
- \(-y=6\)
- \(-v=-72\)
- \(-\frac{5}{8} w=40\)
- \(-\frac{2}{5}=\frac{1}{10} a\)
- \(100-16=4 p-10 p-p\)
- \(\frac{7}{8} n-\frac{3}{4} n=9+2\)
- \(0.25 d+0.10 d=6-0.75\)
- \(-10(q-4)-57=93\)
- \(-10(x+4)-19=85\)
- Answer
-
- \(x=7\)
- \(c=-11\)
- \(y = -\frac{809}{15}\)
- \(p=\frac{541}{37}\)
- z= 13
- \(x=0\)
- \(x=140\)
- \(q=100\)
- \(y=-144\)
- \(m=-540\)
- \(y=-6\)
- \(v=72\)
- \(w=-64\)
- \(a=-4\)
- \(p=-12\)
- \(n=88\)
- d=15
- \(q=-11\)
- \(x=-\frac{72}{5}\)
- Construction Miguel wants to drill a hole for a \(\frac{5}{8}\) inch screw. The hole should be \(\frac{1}{12}\) inch smaller than the screw. Let \(d\) equal the size of the hole he should drill. Solve the equation \(d=\frac{5}{8}-\frac{1}{12}\) to see what size the hole should be.
- Baking Kelsey needs \(\frac{2}{3}\) cup of sugar for the cookie recipe she wants to make. She only has \(\frac{3}{8}\) cup of sugar and will borrow the rest from her ner neighbor. Let \(s\) equal the amount of sugar she will borrow. Solve the equation \(\frac{3}{8}+s=\frac{2}{3}\) to find the amount of sugar she should ask to borrow.
- Commissions Every week Perry gets paid \(\$150\) plus 12% of his total sales amount. Solve the equation \(840=150+0.12(a-1250)\) for \(a\) to find the total amount Perry must sell in order to be paid \(\$ 840\) one week.
- Stamps Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s, to find the number of 49-cent stamps Travis bought.
- Answer
-
- \(d=\frac{13}{24}\) inch
- \(s=\frac{7}{24}\) cups
- \(a=7000\)
- 15 49-cent stamps