Make X The Subject Of The Formula.(a) R − 5 X = T R - 5x = T R − 5 X = T Solve For X: X = T − R − 5 X = \frac{t - R}{-5} X = − 5 T − R ​ (b) M + X N = P M + \frac{x}{n} = P M + N X ​ = P Solve For X:(Note: Further Steps To Solve This Equation Can Be Provided If Needed.)

Introduction

In algebra, solving for x is a crucial step in understanding and manipulating equations. It involves isolating the variable x on one side of the equation, while keeping the other variables on the other side. In this article, we will explore two different algebraic equations and learn how to solve for x in each of them.

Equation (a): Solving for x in $r - 5x = t$

The first equation we will solve is $r - 5x = t$. To solve for x, we need to isolate x on one side of the equation. We can start by adding $5x$ to both sides of the equation, which will eliminate the negative term.

r - 5x + 5x = t + 5x

This simplifies to:

r = t + 5x

Next, we can subtract $t$ from both sides of the equation to get:

r - t = 5x

Finally, we can divide both sides of the equation by $5$ to solve for x:

x = \frac{r - t}{5}

However, the original problem statement asks us to solve for x in the equation $r - 5x = t$. To match this, we can multiply both sides of the equation by $-1$:

-1(r - 5x) = -1t

This simplifies to:

- r + 5x = -t

Next, we can add $r$ to both sides of the equation to get:

5x = r - t

Finally, we can divide both sides of the equation by $5$ to solve for x:

x = \frac{t - r}{-5}

Equation (b): Solving for x in $m + \frac{x}{n} = p$

The second equation we will solve is $m + \frac{x}{n} = p$. To solve for x, we need to isolate x on one side of the equation. We can start by subtracting $m$ from both sides of the equation, which will eliminate the constant term.

m + \frac{x}{n} - m = p - m

This simplifies to:

\frac{x}{n} = p - m

Next, we can multiply both sides of the equation by $n$ to get:

x = n(p - m)

However, the original problem statement asks us to solve for x in the equation $m + \frac{x}{n} = p$. To match this, we can multiply both sides of the equation by $n$:

n(m + \frac{x}{n}) = n(p)

This simplifies to:

nm + x = np

Next, we can subtract $nm$ from both sides of the equation to get:

x = np - nm

Finally, we can factor out $m$ from the right-hand side of the equation to get:

x = m(n - 1)p

However, this is not the solution we are looking for. To solve for x, we need to isolate x on one side of the equation. We can start by subtracting $m$ from both sides of the equation, which will eliminate the constant term.

m + \frac{x}{n} - m = p - m

This simplifies to:

\frac{x}{n} = p - m

Next, we can multiply both sides of the equation by $n$ to get:

x = n(p - m)

However, we can simplify this further by distributing the $n$ to the terms inside the parentheses:

x = np - nm

This is the solution we are looking for.

Conclusion

Solving for x in algebraic equations is a crucial step in understanding and manipulating equations. In this article, we learned how to solve for x in two different algebraic equations. We started by isolating x on one side of the equation, and then used algebraic properties to simplify the equation and solve for x. By following these steps, we can solve for x in a variety of algebraic equations.

Additional Tips and Tricks

• When solving for x, it's often helpful to isolate x on one side of the equation.
• Use algebraic properties such as addition, subtraction, multiplication, and division to simplify the equation.
• Be careful when multiplying or dividing both sides of the equation by a variable or expression.
• Use parentheses to group terms and avoid confusion.
• Check your work by plugging the solution back into the original equation.

Practice Problems

1. Solve for x in the equation $2x + 5 = 11$.
2. Solve for x in the equation $x - 3 = 7$.
3. Solve for x in the equation $x + \frac{2}{3} = 5$.

Answer Key

1. $x = 3$
2. $x = 10$
3. $x = \frac{13}{3}$
   Frequently Asked Questions (FAQs) about Solving for x =====================================================

Q: What is solving for x?

A: Solving for x is a process in algebra where you isolate the variable x on one side of the equation, while keeping the other variables on the other side. This involves using algebraic properties such as addition, subtraction, multiplication, and division to simplify the equation and solve for x.

Q: How do I start solving for x?

A: To start solving for x, you need to isolate x on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by a variable or expression.

Q: What are some common mistakes to avoid when solving for x?

A: Some common mistakes to avoid when solving for x include:

• Not isolating x on one side of the equation
• Not using parentheses to group terms
• Not checking your work by plugging the solution back into the original equation
• Not being careful when multiplying or dividing both sides of the equation by a variable or expression

Q: How do I know if I have solved for x correctly?

A: To know if you have solved for x correctly, you need to check your work by plugging the solution back into the original equation. If the solution satisfies the equation, then you have solved for x correctly.

Q: What are some tips for solving for x in more complex equations?

A: Some tips for solving for x in more complex equations include:

• Breaking down the equation into smaller parts
• Using algebraic properties such as addition, subtraction, multiplication, and division to simplify the equation
• Using parentheses to group terms
• Checking your work by plugging the solution back into the original equation

Q: Can I use a calculator to solve for x?

A: Yes, you can use a calculator to solve for x. However, it's always a good idea to check your work by plugging the solution back into the original equation to make sure you have solved for x correctly.

Q: How do I solve for x in an equation with fractions?

A: To solve for x in an equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the denominator of the fraction.

Q: How do I solve for x in an equation with decimals?

A: To solve for x in an equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by a power of 10.

Q: Can I solve for x in an equation with variables on both sides?

A: Yes, you can solve for x in an equation with variables on both sides. You need to isolate x on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by a variable or expression.

Q: How do I solve for x in an equation with exponents?

A: To solve for x in an equation with exponents, you need to eliminate the exponents by using the properties of exponents.

Q: Can I solve for x in an equation with absolute values?

A: Yes, you can solve for x in an equation with absolute values. You need to isolate x on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by a variable or expression.

Q: How do I solve for x in an equation with inequalities?

A: To solve for x in an equation with inequalities, you need to isolate x on one side of the inequality by adding, subtracting, multiplying, or dividing both sides of the inequality by a variable or expression.

Conclusion

Solving for x is a crucial step in algebra that involves isolating the variable x on one side of the equation. By following the tips and tricks outlined in this article, you can solve for x in a variety of algebraic equations. Remember to check your work by plugging the solution back into the original equation to make sure you have solved for x correctly.