Addition and Subtraction of Directed Numbers: Worded problems

To solve this problem, let's work through it step-by-step:

• Step 1: Identify what Daniel has and what he wants to do.
• Step 2: Use the subtraction operation to calculate the money left after the purchase.

Step 1: Daniel starts with $\$10$.
Step 2: He wants to buy cookies costing $\$20$.

Using the subtraction formula to find the remaining money:

$\text{Remaining Money} = \$10 - \$20$

This calculation yields:

$\$10 - \$20 = -\$10$

This result means Daniel will have $-\$10$ left, indicating he lacks $10 to make this purchase.

The correct solution to the problem is $\boxed{-10}$.

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

• Step 1: Set up the equation based on the problem statement.
• Step 2: Solve the equation step-by-step.
• Step 3: Compare with the answer choices to select the correct option.

Now, let's work through each step:

Step 1: The problem gives us the equation $-2 - x = 10$.

Step 2: To isolate $x$, we start by adding $2$ to both sides of the equation: $-2 - x + 2 = 10 + 2$ $-x = 12$

Then, multiply both sides by $-1$ to solve for $x$: $x = -12 \times -1$ $x = -12$

Step 3: Therefore, when $x = -12$, it satisfies the condition that $-2 - (-12) = 10$.

Therefore, the solution to the problem is $x = 8$.

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

• Step 1: Set up the equation based on the problem statement.
• Step 2: Solve the equation algebraically for $x$.
• Step 3: Verify the solution using the context of the problem.

Now, let's work through each step:
Step 1: Based on the problem, we have the equation:
$x - 5 = 41$ Step 2: To solve for $x$, add 5 to both sides of the equation to get:
$x - 5 + 5 = 41 + 5$
Which simplifies to:
$x = 46$ Step 3: To verify, substitute 46 back into the context of the problem:
Subtract 5 from 46, which gives us:
$46 - 5 = 41$
This confirms our solution is consistent with the problem statement.

Therefore, the solution to the problem is $x = 46$.

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 $x = -33$.

To solve this problem, we begin by formulating it as an algebraic equation based on the information given. We are asked to find a number such that adding -4 to it yields 7. Mathematically, this can be expressed as:

$x + (-4) = 7$

which simplifies to:

$x - 4 = 7$

We solve for $x$ by adding 4 to both sides of the equation to isolate the variable:

• $x - 4 + 4 = 7 + 4$

This results in:

$x = 11$

Therefore, the number we are looking for is $11$.

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

• Step 1: Set up the equation using the given information.
• Step 2: Rearrange the equation to solve for $x$.
• Step 3: Calculate the value of $x$.

Now, let's work through each step:

Step 1: We are given that adding $-3$ to a number $x$ results in $-24$. This can be written as:
$x + (-3) = -24$.

Step 2: To isolate $x$, we add 3 to both sides of the equation, as $-3$ is the term being added:
$x + (-3) + 3 = -24 + 3$.

Step 3: Simplifying the equation gives us:
$x = -24 + 3$.
Perform the addition on the right-hand side:
$x = -21$.

Therefore, the solution to the problem is that the number is $-21$.

To solve this problem, we need to follow these steps:

• Step 1: Write down the equation representing the problem: $x + (-5) = -17$.
• Step 2: Isolate the variable $x$ by performing basic arithmetic operations.

Now, let's work through each step:

Step 1: The equation given by the problem is $x + (-5) = -17$. This means we need to find a number $x$ that, when -5 is added, results in -17.

Step 2: To solve for $x$, we need to isolate it. We can do this by adding 5 to both sides of the equation:

$x + (-5) + 5 = -17 + 5$

On the left side, adding 5 cancels out the -5, leaving us with:

$x = -17 + 5$

Now, perform the arithmetic operation on the right-hand side:

$-17 + 5 = -12$

Therefore, the number we are looking for is $x = -12$.

Thus, the solution to the problem is $-12$.