Question

in 9 - 14, solve and graph your solution on the given number line.

1. ( s + 8.8 lt 4.76 )
2. ( t + 12.3 gt 9\frac{3}{10} )
3. ( u + - 8.01 geq - 8.01 )
4. ( v + - 9.4 geq - 6.2 )
5. ( w + 18.68 leq 12.4 )
6. ( x + 3 lt 8 - 5 )
7. multiple choice. which of the following are solutions to ( - 21.3 + x lt 1.3 )? there may be more than one correct answer.

a - 20
b 20
c - 22.6
d 22.6
e 40
f - 40

1. shyamala will be able to visit an out - of - town friend this summer if she saves up some money. the trip will cost at least $150. so far, she has saved $52, and she expects to save $6 each week from her allowance. if the trip will take place 9 weeks from today, how much more money will shyamala need at the time she leaves for the trip?

a. write an inequality to answer the question.
b. solve your inequality.

1. john has scores of 98, 88, 95, 85, and 92 on five math tests. his total number of points for six tests must be at least 546 in order for his average score to be at least 91. what score must he get on the sixth test to achieve his goal?

a. write an inequality to answer the question.

Explanation:

Step1: Solve the inequality \(s + 8.8<4.76\)

Subtract \(8.8\) from both sides.
\(s+8.8 - 8.8<4.76 - 8.8\)
\(s<-4.04\)

Step2: Graph the solution \(s < - 4.04\)

On the number - line, draw an open circle at \(-4.04\) (because the inequality is strict, \(s
eq - 4.04\)) and shade to the left.

Step3: Solve the inequality \(t + 12.3>9\frac{3}{10}\)

First, convert \(9\frac{3}{10}=9.3\). Then subtract \(12.3\) from both sides.
\(t+12.3-12.3>9.3 - 12.3\)
\(t>-3\)

Step4: Graph the solution \(t > - 3\)

On the number - line, draw an open circle at \(-3\) (because \(t
eq - 3\)) and shade to the right.

Step5: Solve the inequality \(u+( - 8.01)\geq - 8.01\)

Add \(8.01\) to both sides.
\(u-8.01 + 8.01\geq - 8.01+8.01\)
\(u\geq0\)

Step6: Graph the solution \(u\geq0\)

On the number - line, draw a closed circle at \(0\) (because \(u = 0\) is included in the solution) and shade to the right.

Step7: Solve the inequality \(v+( - 9.4)\geq - 6.2\)

Add \(9.4\) to both sides.
\(v-9.4 + 9.4\geq - 6.2+9.4\)
\(v\geq3.2\)

Step8: Graph the solution \(v\geq3.2\)

On the number - line, draw a closed circle at \(3.2\) (because \(v = 3.2\) is included in the solution) and shade to the right.

Step9: Solve the inequality \(w + 18.68\leq12.4\)

Subtract \(18.68\) from both sides.
\(w+18.68-18.68\leq12.4 - 18.68\)
\(w\leq - 6.28\)

Step10: Graph the solution \(w\leq - 6.28\)

On the number - line, draw a closed circle at \(-6.28\) (because \(w=-6.28\) is included in the solution) and shade to the left.

Step11: Solve the inequality \(x + 3<8 - 5\)

First, simplify the right - hand side: \(8 - 5=3\). Then subtract \(3\) from both sides.
\(x+3-3<3 - 3\)
\(x<0\)

Step12: Graph the solution \(x < 0\)

On the number - line, draw an open circle at \(0\) (because \(x
eq0\)) and shade to the left.

Step13: Solve the inequality \(-21.3+x<1.3\)

Add \(21.3\) to both sides.
\(x<1.3 + 21.3\)
\(x<22.6\)
Check the options:

• For \(x=-20\), \(-20<22.6\)
• For \(x = 20\), \(20<22.6\)
• For \(x=-22.6\), \(-22.6<22.6\)
• For \(x = 22.6\), \(22.6

ot<22.6\)

• For \(x = 40\), \(40

ot<22.6\)

• For \(x=-40\), \(-40<22.6\)

Step14: Solve problem 16a

Let \(x\) be the additional money needed. The money she has saved plus the money she will save (\(6\times9\)) must be at least \(150\). The inequality is \(52+6\times9+x\geq150\)

Step15: Solve problem 16b

Simplify \(52 + 54+x\geq150\), \(106+x\geq150\). Subtract \(106\) from both sides: \(x\geq44\)

Step16: Solve problem 17a

Let \(x\) be the score on the sixth test. The sum of the first five scores (\(98 + 88+95+85+92\)) plus \(x\) must be at least \(546\). The sum of the first five scores is \(98+88+95+85+92=(98 + 88)+(95+85)+92=186+180+92=458\). The inequality is \(458+x\geq546\)

Answer:

1. \(s < - 4.04\) (open circle at \(-4.04\), shade left)
2. \(t > - 3\) (open circle at \(-3\), shade right)
3. \(u\geq0\) (closed circle at \(0\), shade right)
4. \(v\geq3.2\) (closed circle at \(3.2\), shade right)
5. \(w\leq - 6.28\) (closed circle at \(-6.28\), shade left)
6. \(x < 0\) (open circle at \(0\), shade left)
7. A. \(-20\), B. \(20\), C. \(-22.6\), F. \(-40\)

16a. \(52+6\times9+x\geq150\)
16b. \(x\geq44\)
17a. \(458+x\geq546\)