Solve for X: X - (-14) = -19 in Integer Operations

Q: Why does subtracting a negative number become addition?

Think of it this way: if you remove a debt (negative), you're actually gaining money (positive)! So $ x - (-14) $ means 'x minus negative 14' which equals 'x plus 14'.

Q: How can I remember the double negative rule?

Use the phrase 'minus a minus makes a plus'! Two negative signs next to each other always become positive: $ -(-14) = +14 $.

Q: What if I get confused with all the negative signs?

Break it down step by step: First identify what operation you're doing (subtraction), then what number you're subtracting (negative 14). Finally, apply the rule that subtracting negative = adding positive.

Q: How do I check if x = -33 is really correct?

Substitute back into the original: $ -33 - (-14) = -33 + 14 = -19 $. Since this equals the right side of our equation, -33 is correct!

Q: Why is the answer negative when we're adding 14?

Even though we add 14, we start with $ x + 14 = -19 $, so we need $ x = -19 - 14 = -33 $. The negative answer makes sense because we need a number that becomes -19 when increased by 14.

Integer Subtraction with Double Negatives

Which number results in -19 when you subtract -14 from it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:04 Negative times negative always equals positive

00:07 Open parentheses

00:12 Isolate the unknown

00:26 Calculate each operation separately

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which number results in -19 when you subtract -14 from it?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Recognize the relevant formula and rewrite the equation.
Step 2: Perform the arithmetic calculations to find $x$ .

Now, let's work through each step:
Step 1: We rewrite the equation $x - (-14) = -19$ as $x + 14 = -19$ .
Step 2: To solve for $x$ , we subtract 14 from both sides:
$x + 14 - 14 = -19 - 14$
This simplifies to:
$x = -19 - 14 = -33$ .

Therefore, the solution to the problem is $x = -33$ .

Final Answer

$-33$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtracting negative numbers means adding the positive value
Technique: Rewrite x - (-14) = -19 as x + 14 = -19
Check: Substitute -33: -33 - (-14) = -33 + 14 = -19 ✓

Common Mistakes

Avoid these frequent errors

Treating double negative as subtraction
Don't change x - (-14) to x - 14 = -33! This ignores the rule that subtracting a negative equals adding positive, giving you the wrong answer of -5 instead of -33. Always remember: minus a negative becomes plus a positive.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why does subtracting a negative number become addition?

Think of it this way: if you remove a debt (negative), you're actually gaining money (positive)! So $x - (-14)$ means 'x minus negative 14' which equals 'x plus 14'.

How can I remember the double negative rule?

Use the phrase 'minus a minus makes a plus'! Two negative signs next to each other always become positive: $-(-14) = +14$ .

What if I get confused with all the negative signs?

Break it down step by step: First identify what operation you're doing (subtraction), then what number you're subtracting (negative 14). Finally, apply the rule that subtracting negative = adding positive.

How do I check if x = -33 is really correct?

Substitute back into the original: $-33 - (-14) = -33 + 14 = -19$ . Since this equals the right side of our equation, -33 is correct!

Why is the answer negative when we're adding 14?

Even though we add 14, we start with $x + 14 = -19$ , so we need $x = -19 - 14 = -33$ . The negative answer makes sense because we need a number that becomes -19 when increased by 14.

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