Questions: Question 2 For each of the following, determine if the given value is a solution to the equation. a. Is x=12.6 a solution to 2.9x+1.46=23.41+x ? Select an answer b. Is b=-2.2 a solution to 3.5x+4.3=2.1x+1.22 ? Select an answer

Question 2 For each of the following, determine if the given value is a solution to the equation. a. Is x=12.6 a solution to 2.9x+1.46=23.41+x ? Select an answer b. Is b=-2.2 a solution to 3.5x+4.3=2.1x+1.22 ? Select an answer
Transcript text: Question 2 For each of the following, determine if the given value is a solution to the equation. a. Is $x=12.6$ a solution to $2.9 x+1.46=23.41+x$ ? Select an answer b. Is $b=-2.2$ a solution to $3.5 x+4.3=2.1 x+1.22$ ? Select an answer
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Solution

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Solution Steps

To determine if a given value is a solution to an equation, substitute the value into the equation and check if both sides are equal.

Part (a)
  1. Substitute \( x = 12.6 \) into the equation \( 2.9x + 1.46 = 23.41 + x \).
  2. Simplify both sides and check if they are equal.
Part (b)
  1. Substitute \( b = -2.2 \) into the equation \( 3.5x + 4.3 = 2.1x + 1.22 \).
  2. Simplify both sides and check if they are equal.
Step 1: Substitute \( x = 12.6 \) into the equation \( 2.9x + 1.46 = 23.41 + x \)

Substitute \( x = 12.6 \) into the left side of the equation: \[ 2.9 \times 12.6 + 1.46 = 36.54 + 1.46 = 38.00 \]

Substitute \( x = 12.6 \) into the right side of the equation: \[ 23.41 + 12.6 = 36.01 \]

Step 2: Compare both sides for \( x = 12.6 \)

Since \( 38.00 \neq 36.01 \), \( x = 12.6 \) is not a solution to the equation \( 2.9x + 1.46 = 23.41 + x \).

\[ \boxed{\text{No}} \]

Step 3: Substitute \( b = -2.2 \) into the equation \( 3.5x + 4.3 = 2.1x + 1.22 \)

Substitute \( b = -2.2 \) into the left side of the equation: \[ 3.5 \times (-2.2) + 4.3 = -7.7 + 4.3 = -3.4 \]

Substitute \( b = -2.2 \) into the right side of the equation: \[ 2.1 \times (-2.2) + 1.22 = -4.62 + 1.22 = -3.4 \]

Step 4: Compare both sides for \( b = -2.2 \)

Since \( -3.4 = -3.4 \), \( b = -2.2 \) is a solution to the equation \( 3.5x + 4.3 = 2.1x + 1.22 \).

\[ \boxed{\text{Yes}} \]

Final Answer

\[ \boxed{\text{No}} \]

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