Question

solve the equations
round your answers to the nearest hundredth if needed.

1. - 8(5 + 6f)=-26

-40 - 48f=-26
+40 +40
-48f = 14
-48 -48
f = -7/24

1. -18 = 8 + 5(k - 9)

-18 = 8+5k - 45
-18=-37 + 5k
+37 +37
19 = 5k
19/5 = 5k/5
k = 19/5

1. 7(3c + 8)=20 - 4c

21c + 56 = 20 - 4c

1. -9d - 5 - 6d=-23
2. -28=-6b + 7b
3. -5(1 + 7x)=-24

-5 - 35x=-24
+5 +5
-35x=-19
-35 -35
x = 19/35

1. 6y - 3y = 22
2. 9 + 4(1 - 7z)=33
3. 5s - 3 + 9 = 32
4. -6(5r - 4)=20

-30r+24 = 20
+24 +24
-30r = 44
-30 -30
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Explanation:

Step1: Expand the equation

For equation \(7(3c + 8)=20 - 4c\), use the distributive - property \(a(b + c)=ab+ac\). So, \(7\times3c+7\times8 = 20 - 4c\), which simplifies to \(21c + 56=20 - 4c\).

Step2: Move variable terms to one side

Add \(4c\) to both sides of the equation: \(21c+4c + 56=20-4c + 4c\), resulting in \(25c+56 = 20\).

Step3: Move constant terms to the other side

Subtract 56 from both sides: \(25c+56 - 56=20 - 56\), giving \(25c=-36\).

Step4: Solve for the variable

Divide both sides by 25: \(c=\frac{-36}{25}=-1.44\).

For equation \(-9d-5 - 6d=-23\):

Step1: Combine like - terms

Combine the \(d\) terms: \((-9d-6d)-5=-23\), which simplifies to \(-15d-5=-23\).

Step2: Move the constant term

Add 5 to both sides: \(-15d-5 + 5=-23 + 5\), resulting in \(-15d=-18\).

Step3: Solve for the variable

Divide both sides by \(-15\): \(d=\frac{-18}{-15}=\frac{6}{5}=1.2\).

For equation \(-28=-6b + 7b\):

Step1: Combine like - terms

\(-6b + 7b=b\), so \(b=-28\).

For equation \(6y-3y = 22\):

Step1: Combine like - terms

\(6y-3y = 3y\), so \(3y=22\).

Step2: Solve for the variable

\(y=\frac{22}{3}\approx7.33\).

For equation \(9 + 4(1 - 7z)=33\):

Step1: Expand the equation

Use the distributive property: \(9+4\times1-4\times7z=33\), which simplifies to \(9 + 4-28z=33\), or \(13-28z=33\).

Step2: Move the constant term

Subtract 13 from both sides: \(13-13-28z=33 - 13\), resulting in \(-28z=20\).

Step3: Solve for the variable

\(z=\frac{20}{-28}=-\frac{5}{7}\approx - 0.71\).

For equation \(5s-3 + 9=32\):

Step1: Combine constant terms

\(-3 + 9 = 6\), so the equation becomes \(5s+6=32\).

Step2: Move the constant term

Subtract 6 from both sides: \(5s+6 - 6=32 - 6\), resulting in \(5s=26\).

Step3: Solve for the variable

\(s=\frac{26}{5}=5.2\).

For equation \(-6(5r-4)=20\):

Step1: Expand the equation

\(-6\times5r-6\times(-4)=20\), which simplifies to \(-30r + 24=20\).

Step2: Move the constant term

Subtract 24 from both sides: \(-30r+24 - 24=20 - 24\), resulting in \(-30r=-4\).

Step3: Solve for the variable

\(r=\frac{-4}{-30}=\frac{2}{15}\approx0.13\).

Answer:

1. \(f =-\frac{7}{24}\approx - 0.29\)
2. \(k=\frac{19}{5}=3.8\)
3. \(c=-1.44\)
4. \(d = 1.2\)
5. \(b=-28\)
6. \(x=\frac{19}{35}\approx0.54\)
7. \(y=\frac{22}{3}\approx7.33\)
8. \(z=-\frac{5}{7}\approx - 0.71\)
9. \(s = 5.2\)
10. \(r=\frac{2}{15}\approx0.13\)