chapter 1 test: solving equations
you must show your work for full credit!
solve.
1. ( \frac{4}{5} = b )
2. ( -4 = 3x + 5 )
3. ( -2(-6y + 4) - 6 = 34 )
4. ( 5c + 3 = 24 - 2c )
5. if ( i = prt ), solve for ( t ).
6. the sum of the angles in a rectangle is 360°. write an equation and solve for ( x ) using the diagram.
(diagram: rectangle with angles ( (x+46)^circ ), ( x^circ ), ( (x+39)^circ ), ( (x+27)^circ ))

Question

Accepted Answer

### Problem 1: Solve $\frac{4}{5} = B$
# Explanation:
## Step 1: Identify the equation
The equation is already in a form where $B$ is isolated. So $B$ is equal to $\frac{4}{5}$.
# Answer:
$B = \frac{4}{5}$

### Problem 2: Solve $-4 = 3x + 5$
# Explanation:
## Step 1: Subtract 5 from both sides
To isolate the term with $x$, we subtract 5 from both sides of the equation.
$-4 - 5=3x + 5 - 5$
$-9 = 3x$
## Step 2: Divide by 3
Divide both sides by 3 to solve for $x$.
$\frac{-9}{3}=\frac{3x}{3}$
$-3 = x$
# Answer:
$x=-3$

### Problem 3: Solve $-2(-6y + 4)-6 = 34$
# Explanation:
## Step 1: Distribute -2
First, distribute the -2 across the terms inside the parentheses.
$(-2)\times(-6y)+(-2)\times4 - 6=34$
$12y-8 - 6 = 34$
## Step 2: Combine like terms
Combine the constant terms on the left side.
$12y-(8 + 6)=34$
$12y-14 = 34$
## Step 3: Add 14 to both sides
Add 14 to both sides to isolate the term with $y$.
$12y-14 + 14=34 + 14$
$12y=48$
## Step 4: Divide by 12
Divide both sides by 12 to solve for $y$.
$\frac{12y}{12}=\frac{48}{12}$
$y = 4$
# Answer:
$y = 4$

### Problem 4: Solve $5c+3 = 24-2c$
# Explanation:
## Step 1: Add $2c$ to both sides
To get all the $c$ terms on one side, add $2c$ to both sides.
$5c+2c + 3=24-2c+2c$
$7c + 3=24$
## Step 2: Subtract 3 from both sides
Subtract 3 from both sides to isolate the term with $c$.
$7c+3 - 3=24 - 3$
$7c=21$
## Step 3: Divide by 7
Divide both sides by 7 to solve for $c$.
$\frac{7c}{7}=\frac{21}{7}$
$c = 3$
# Answer:
$c = 3$

### Problem 5: If $I = Prt$, solve for $t$
# Explanation:
## Step 1: Divide both sides by $Pr$
To isolate $t$, we divide both sides of the equation $I = Prt$ by $Pr$ (assuming $Pr
eq0$).
$\frac{I}{Pr}=\frac{Prt}{Pr}$
$t=\frac{I}{Pr}$
# Answer:
$t=\frac{I}{Pr}$

### Problem 6: The sum of the angles in a rectangle is $360^{\circ}$. Write an equation and solve for $x$ using the diagram with angles $(x + 46)^{\circ}$, $x^{\circ}$, $(x + 39)^{\circ}$, and $(x + 27)^{\circ}$
# Explanation:
## Step 1: Set up the equation
The sum of the four angles in a rectangle is $360^{\circ}$. So we add the four angle expressions and set them equal to $360$.
$(x + 46)+x+(x + 39)+(x + 27)=360$
## Step 2: Combine like terms
Combine the $x$ terms and the constant terms.
$(x+x+x+x)+(46 + 39+27)=360$
$4x+112 = 360$
## Step 3: Subtract 112 from both sides
Subtract 112 from both sides to isolate the term with $x$.
$4x+112 - 112=360 - 112$
$4x=248$
## Step 4: Divide by 4
Divide both sides by 4 to solve for $x$.
$\frac{4x}{4}=\frac{248}{4}$
$x = 62$
# Answer:
The equation is $(x + 46)+x+(x + 39)+(x + 27)=360$ and $x = 62$

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QUESTION IMAGE

Question

Explanation:

Problem 1: Solve \(\frac{4}{5} = B\)

Step 1: Identify the equation

Step 1: Subtract 5 from both sides

Step 2: Divide by 3

Step 1: Distribute -2

Step 2: Combine like terms

Step 3: Add 14 to both sides

Step 4: Divide by 12

Answer:

Problem 2: Solve \(-4 = 3x + 5\)