IDNLearn.com connects you with experts who provide accurate and reliable answers. Our platform offers reliable and detailed answers, ensuring you have the information you need.
Sagot :
Alright, let's go through these equations step-by-step to solve for [tex]\( x \)[/tex].
### 3.1.1 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ \frac{x}{8} + 9 = 2 \][/tex]
1. Subtract 9 from both sides to isolate the fraction:
[tex]\[ \frac{x}{8} = 2 - 9 \][/tex]
[tex]\[ \frac{x}{8} = -7 \][/tex]
2. Multiply both sides by 8 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = -7 \times 8 \][/tex]
[tex]\[ x = -56 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( -56 \)[/tex] in this equation.
### 3.1.25 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ x = 40 + 3x \][/tex]
1. Subtract [tex]\( 3x \)[/tex] from both sides to get the [tex]\( x \)[/tex] terms on one side:
[tex]\[ x - 3x = 40 \][/tex]
[tex]\[ -2x = 40 \][/tex]
2. Divide both sides by [tex]\(-2\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{40}{-2} \][/tex]
[tex]\[ x = -20 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( -20 \)[/tex] in this equation.
### 3.1.38 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ 8^x = 32 \][/tex]
1. Rewrite both sides using a common base. Since [tex]\( 8 = 2^3 \)[/tex] and [tex]\( 32 = 2^5 \)[/tex], we can rewrite the equation as:
[tex]\[ (2^3)^x = 2^5 \][/tex]
[tex]\[ 2^{3x} = 2^5 \][/tex]
2. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ 3x = 5 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5}{3} \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( \frac{5}{3} \)[/tex] (or approximately [tex]\( 1.67 \)[/tex]) in this equation.
### 3.1.42 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ x - 3 = 14 \][/tex]
1. Add 3 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 14 + 3 \][/tex]
[tex]\[ x = 17 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( 17 \)[/tex] in this equation.
### 3.1.5 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ \frac{3x - 1}{2} = 4 \][/tex]
1. Multiply both sides by 2 to eliminate the denominator:
[tex]\[ 3x - 1 = 4 \times 2 \][/tex]
[tex]\[ 3x - 1 = 8 \][/tex]
2. Add 1 to both sides to isolate the [tex]\( 3x \)[/tex] term:
[tex]\[ 3x = 8 + 1 \][/tex]
[tex]\[ 3x = 9 \][/tex]
3. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{9}{3} \][/tex]
[tex]\[ x = 3 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex] in this equation.
In summary, the solutions for [tex]\( x \)[/tex] in the given equations are:
1. [tex]\( x = -56 \)[/tex]
2. [tex]\( x = -20 \)[/tex]
3. [tex]\( x = \frac{5}{3} \)[/tex] (or approximately [tex]\( 1.67 \)[/tex])
4. [tex]\( x = 17 \)[/tex]
5. [tex]\( x = 3 \)[/tex]
### 3.1.1 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ \frac{x}{8} + 9 = 2 \][/tex]
1. Subtract 9 from both sides to isolate the fraction:
[tex]\[ \frac{x}{8} = 2 - 9 \][/tex]
[tex]\[ \frac{x}{8} = -7 \][/tex]
2. Multiply both sides by 8 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = -7 \times 8 \][/tex]
[tex]\[ x = -56 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( -56 \)[/tex] in this equation.
### 3.1.25 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ x = 40 + 3x \][/tex]
1. Subtract [tex]\( 3x \)[/tex] from both sides to get the [tex]\( x \)[/tex] terms on one side:
[tex]\[ x - 3x = 40 \][/tex]
[tex]\[ -2x = 40 \][/tex]
2. Divide both sides by [tex]\(-2\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{40}{-2} \][/tex]
[tex]\[ x = -20 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( -20 \)[/tex] in this equation.
### 3.1.38 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ 8^x = 32 \][/tex]
1. Rewrite both sides using a common base. Since [tex]\( 8 = 2^3 \)[/tex] and [tex]\( 32 = 2^5 \)[/tex], we can rewrite the equation as:
[tex]\[ (2^3)^x = 2^5 \][/tex]
[tex]\[ 2^{3x} = 2^5 \][/tex]
2. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ 3x = 5 \][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5}{3} \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( \frac{5}{3} \)[/tex] (or approximately [tex]\( 1.67 \)[/tex]) in this equation.
### 3.1.42 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ x - 3 = 14 \][/tex]
1. Add 3 to both sides to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 14 + 3 \][/tex]
[tex]\[ x = 17 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( 17 \)[/tex] in this equation.
### 3.1.5 Solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ \frac{3x - 1}{2} = 4 \][/tex]
1. Multiply both sides by 2 to eliminate the denominator:
[tex]\[ 3x - 1 = 4 \times 2 \][/tex]
[tex]\[ 3x - 1 = 8 \][/tex]
2. Add 1 to both sides to isolate the [tex]\( 3x \)[/tex] term:
[tex]\[ 3x = 8 + 1 \][/tex]
[tex]\[ 3x = 9 \][/tex]
3. Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{9}{3} \][/tex]
[tex]\[ x = 3 \][/tex]
So, [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex] in this equation.
In summary, the solutions for [tex]\( x \)[/tex] in the given equations are:
1. [tex]\( x = -56 \)[/tex]
2. [tex]\( x = -20 \)[/tex]
3. [tex]\( x = \frac{5}{3} \)[/tex] (or approximately [tex]\( 1.67 \)[/tex])
4. [tex]\( x = 17 \)[/tex]
5. [tex]\( x = 3 \)[/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.
