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1 month ago

Match each step to its justification to solve 2x+5=19

Mathematics

2 answers:

tester [12.3K]1 month ago

6 0

The process involves:

starting information
principle of subtraction within equality
deducting
principle of division within equality
dividing

Additional Details

A linear equation with one variable consists of one variable raised to the power of one. It can be expressed as:

$\large{\boxed{\bold{ax=b}}}$

ax + b = c, where a, b, and c are fixed figures, and x stands for a variable.

On the other hand, a linear equation with two variables features two variables, both raised to the first power.

It can be articulated in the form:

$\large{\boxed{\bold{ax+by=c}}}$

ax + by = c

where x and y are the variables.

To solve a linear equation with a single variable, you typically follow two main steps:

1. Adjust both sides by adding or subtracting the same value, leaving only the variable terms or constant numbers on one side.

2. Reform the equation so that the coefficient of the variable equals 1.

This can be achieved through division or multiplication by equivalent values.

The equation will retain its equivalency if both sides are multiplied or divided by the same quantity.

As seen in the equation:

2x + 5 = 19

The correct process to solve it, according to the accompanying visuals, includes:

1. 2x + 5 = 19 ⇒ initial condition

2. Subtracting 5 from both sides.

2x + 5 - 5 = 19 - 5 ⇒ applying the property of subtraction in equality

3. Thus, 2x = 14 ⇒ deduction step

4. Divide both sides by 2 to have a coefficient of 1 for x.

${\frac {2x} {2}}=~\frac{14}{2$

⇒ applying the property of division in equality

5. Hence, x = 7 ⇒ division step

Additional Information

the slope-intercept form of a linear equation

displaying a graph of a linear equation

systems of linear equations

Keywords: variable, linear equation

Inessa [12.5K]1 month ago

5 0

It includes the procedures to reach that specific point.
Some of them are arranged incorrectly.
I will label them with letters.

The sequence is:
A: 2x+5=19
B: 2x+5-5=19-5
C: 2x=14
D: 2x/2=14/2
E: x=7

A: initial condition
B: we subtracted 5 from both sides based on the subtraction property of equality
C: perform the subtraction
D: applying the division property of equality (dividing both sides by 2)
E: result of the division

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