4(3x+2)=32
17 answers
To solve for \( x \) in the equation \( 4(3x + 2) = 32 \), follow these steps:
Distribute the \( 4 \) on the left side: \[ 4 \cdot 3x + 4 \cdot 2 = 32 \] This simplifies to: \[ 12x + 8 = 32 \]
Subtract \( 8 \) from both sides: \[ 12x + 8 - 8 = 32 - 8 \] This simplifies to: \[ 12x = 24 \]
Divide both sides by \( 12 \): \[ x = \frac{24}{12} \] This simplifies to: \[ x = 2 \]
So, the solution for \( x \) is \( \boxed{2} \).
To solve for \( x \) in the equation \( -2(3x - 15) = 60 \), follow these steps:
Distribute the \(-2\) on the left side: \[ -2 \cdot 3x + (-2) \cdot (-15) = 60 \] This simplifies to: \[ -6x + 30 = 60 \]
Subtract \( 30 \) from both sides: \[ -6x + 30 - 30 = 60 - 30 \] This simplifies to: \[ -6x = 30 \]
Divide both sides by \(-6\): \[ x = \frac{30}{-6} \] This simplifies to: \[ x = -5 \]
So, the solution for \( x \) is \( \boxed{-5} \).
To solve for \( x \) in the equation \( 5(2x - 8) = -30 \), follow these steps:
Distribute the \( 5 \) on the left side: \[ 5 \cdot 2x - 5 \cdot 8 = -30 \] This simplifies to: \[ 10x - 40 = -30 \]
Add \( 40 \) to both sides: \[ 10x - 40 + 40 = -30 + 40 \] This simplifies to: \[ 10x = 10 \]
Divide both sides by \( 10 \): \[ x = \frac{10}{10} \] This simplifies to: \[ x = 1 \]
So, the solution for \( x \) is \( \boxed{1} \).
To solve for \( x \) in the equation \( -4(2x - 11) = 12 \), follow these steps:
Distribute the \(-4\) on the left side: \[ -4 \cdot 2x + (-4) \cdot (-11) = 12 \] This simplifies to: \[ -8x + 44 = 12 \]
Subtract \( 44 \) from both sides: \[ -8x + 44 - 44 = 12 - 44 \] This simplifies to: \[ -8x = -32 \]
Divide both sides by \(-8\): \[ x = \frac{-32}{-8} \] This simplifies to: \[ x = 4 \]
So, the solution for \( x \) is \( \boxed{4} \).
To solve for \( x \) in the equation \( -3(-4x - 3) = -27 \), follow these steps:
Distribute the \(-3\) on the left side: \[ -3 \cdot (-4x) + (-3) \cdot (-3) = -27 \] This simplifies to: \[ 12x + 9 = -27 \]
Subtract \( 9 \) from both sides: \[ 12x + 9 - 9 = -27 - 9 \] This simplifies to: \[ 12x = -36 \]
Divide both sides by \( 12 \): \[ x = \frac{-36}{12} \] This simplifies to: \[ x = -3 \]
So, the solution for \( x \) is \( \boxed{-3} \).
To solve for \( x \) in the equation \( -3(-4x - 3) = -27 \), we will follow these steps:
Distribute the \(-3\) on the left side: \[ -3 \cdot (-4x) - 3 \cdot 3 = -27 \] This expands to: \[ 12x + 9 = -27 \]
Subtract \( 9 \) from both sides: \[ 12x + 9 - 9 = -27 - 9 \] This simplifies to: \[ 12x = -36 \]
Divide both sides by \( 12 \): \[ x = \frac{-36}{12} \] This simplifies to: \[ x = -3 \]
Thus, the solution for \( x \) is \( \boxed{-3} \).
To solve for \( x \) in the equation \( 2x - 4x - 3 = -27 \), follow these steps:
Combine like terms on the left side: \[ (2x - 4x) - 3 = -27 \] This simplifies to: \[ -2x - 3 = -27 \]
Add \( 3 \) to both sides: \[ -2x - 3 + 3 = -27 + 3 \] This simplifies to: \[ -2x = -24 \]
Divide both sides by \(-2\): \[ x = \frac{-24}{-2} \] This simplifies to: \[ x = 12 \]
So, the solution for \( x \) is \( \boxed{12} \).
To solve for \( x \) in the equation \( -4(3x + 10) - 2 = 54 \), follow these steps:
Start by distributing the \(-4\): \[ -4 \cdot 3x - 4 \cdot 10 - 2 = 54 \] This simplifies to: \[ -12x - 40 - 2 = 54 \]
Combine like terms on the left side: \[ -12x - 42 = 54 \]
Now, add \( 42 \) to both sides: \[ -12x - 42 + 42 = 54 + 42 \] This simplifies to: \[ -12x = 96 \]
Divide both sides by \(-12\): \[ x = \frac{96}{-12} \] This simplifies to: \[ x = -8 \]
So, the solution for \( x \) is \( \boxed{-8} \).
To solve for \( x \) in the equation \( 20x - 5(6x + 15) = -45 \), follow these steps:
Distribute the \(-5\) on the left side: \[ 20x - 5 \cdot 6x - 5 \cdot 15 = -45 \] This simplifies to: \[ 20x - 30x - 75 = -45 \]
Combine like terms: \[ (20x - 30x) - 75 = -45 \] This simplifies to: \[ -10x - 75 = -45 \]
Add \( 75 \) to both sides: \[ -10x - 75 + 75 = -45 + 75 \] This simplifies to: \[ -10x = 30 \]
Divide both sides by \(-10\): \[ x = \frac{30}{-10} \] This simplifies to: \[ x = -3 \]
So, the solution for \( x \) is \( \boxed{-3} \).
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