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(4x+3)-(5x-7)=ax+b
In the given equation,
b is a constant. What is the value of
b ?

$(4 x+3)-(5 x-7)=a x+b$ $\newline$ In the given equation, $b$ is a constant. What is the value of $b$ ?

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Write and solve direct variation equations

Full solution

Q.

(4 x+3)-(5 x-7)=a x+b

\newline

In the given equation,

b

is a constant. What is the value of

b

?

Distribute and Simplify: First, we need to simplify the left-hand side of the equation by distributing the negative sign to the terms within the second set of parentheses. This means we will subtract both $5x$ and $-7$ from $4x$ and $3$ , respectively. $\newline$ Calculation: $(4x + 3) - (5x - 7) = 4x + 3 - 5x + 7$
Combine Like Terms: Next, we combine like terms on the left-hand side. This involves combining the $x$ terms and the constant terms separately. $\newline$ Calculation: $(4x - 5x) + (3 + 7) = -x + 10$
Determine Coefficients: Now that we have simplified the left-hand side, we can see that the equation is in the form of $-x + 10 = ax + b$ . Since there is no $x$ term on the right-hand side, we can infer that $a = -1$ . However, we are only interested in the value of $b$ , which is the constant term. $\newline$ Calculation: $b = 10$
Find Constant Term: We have determined that the value of $b$ is $10$ , which is the constant term on the left-hand side after simplification.

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