Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Transcription for Educational Use**
This document seems to contain a series of algebraic equations, along with steps showing their solutions. Below is the transcription and explanation for each problem:
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**Equation 7**:
\[ 3(-2 - 3x) = -9x - 4 \]
Solution Steps:
1. Distribute the 3: \( -6 - 9x = -9x - 4 \)
2. Add 9x to both sides: \( -6 = -4 \)
3. \( x = \) (no solution found)
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**Equation 9**:
\[ 9(4b - 1) = 2(9b + 3) \]
Solution Steps:
1. Distribute: \( 36b - 9 = 18b + 6 \)
2. Rearrange: \( 18b = 15 \)
3. Solve for \( b \): \( b = \frac{15}{18} = \frac{5}{6} \)
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**Equation 11**:
\[ -5x - 10 = 2 - (x + 4) \]
Solution Steps:
1. Expand: \( -5x - 10 = 2 - x - 4 \)
2. Combine like terms: \( -5x - 10 = -x - 2 \)
3. Add 5x and 2 to both sides: \( -10 + x = 8 \)
4. Solve for \( x \): \( x = 8 \)
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**Equation 13**:
\[ \frac{5}{2}t - t = 3 + \frac{3}{2}t \]
Solution Steps:
1. Combine terms: \( \frac{3}{2}t = 3 + \frac{3}{2}t \)
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**Equation 15**:
\[ \frac{2}{3}x - \frac{1}{6} = \frac{1}{2}x + \frac{5}{6} \]
Solution Steps:
1. Rearrange terms.
2. Find a common denominator to solve for \( x \).
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**Equation 17**:
\[ \frac{1}{2}(3g - 2) = \frac{g}{2} \]
Solution Steps:
1. Distribute to clear the fraction.
2. Simplify the equation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F327f750b-9ef8-49e1-8a45-67f289e38396%2F687d3418-d3d7-4b1e-bc39-03e1070b7d9f%2Flpo6yo9_processed.jpeg&w=3840&q=75)
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