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Chapter 2: Problem 354

Solve each equation with decimal coefficients. $$0.6 y+3=9$$

Short Answer

Expert verified
y = 10

Step by step solution

01

Identify Constants and Coefficients

In the equation, identify the decimal coefficient and the constants. The equation is: \(0.6y + 3 = 9\).Here, 0.6 is the coefficient of \(y\), 3 is the constant term on the left side, and 9 is the constant term on the right side.
02

Isolate the Variable Term

Subtract 3 from both sides to isolate the term with the variable:\(0.6y + 3 - 3 = 9 - 3\)This simplifies to:\(0.6y = 6\)
03

Solve for the Variable

Divide both sides by 0.6 to solve for \(y\):\(y = \frac{6}{0.6}\).Simplify the fraction:\(y = 10\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Coefficients
When solving equations, decimal coefficients can sometimes make the process seem tricky. But don't worry! Remember, coefficients are just numbers in front of variables. In the equation given, we have: \[0.6y + 3 = 9\] Here, 0.6 is the decimal coefficient of the variable \(y\). Working with decimals requires careful arithmetic, but the fundamental steps remain consistent, regardless if the coefficient is a whole number or a decimal.
Isolating the Variable
To solve for a variable means to isolate it on one side of the equation. Let's break down the process:

  • Identify the term with the variable. In our case, it's 0.6y.
  • Isolate the variable by moving all other terms to the other side. Subtract 3 from both sides of the equation:
\[0.6y + 3 - 3 = 9 - 3\] This simplifies to:
\[0.6y = 6\] You've successfully isolated the variable term!
Solving Linear Equations
Once the variable is isolated, solving the equation is straightforward:
  • Divide both sides by the coefficient of the variable. In our case, divide by 0.6:
\[y = \frac{6}{0.6}\] Simplifying this, we get:
\[y = 10\]

Always remember:
  • Keep equations balanced by performing the same operation on both sides.
  • Check your solution by plugging it back into the original equation.
Following these steps ensures accuracy and reliability in solving linear equations, even those with decimal coefficients.

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Most popular questions from this chapter

Paula bought $$\$ 22.82$$ worth of 49 -cent stamps and 21 -cent stamps. The number of 21 -cent stamps was 8 less than the number of 49 -cent stamps. Solve the equation \(0.49 s+0.21(s-8)=22.82\) for s, to find the number of 49 -cent stamps Paula bought.

Graph each inequality on the number line and write in interval notation. (a) \(x<-2\) (b) \(\quad x \geq-3.5\) (c) \(x \leq \frac{2}{3}\)

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$-7 d>105$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$9 p>14 p-18$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$5 u \leq 8 u-21$$
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