What number increased by 3 is equal to 3 less than twice the number?

What number increased by 3 is equal to 3 less than twice the number?👇🏾👇🏾👇🏾

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To solve for the number that when increased by 3 equals 3 less than twice the number, we can set up the equation based on the given information.

Let's denote the unknown number by $𝑥$.

The problem states:

• "Increased by 3" can be written as $𝑥+3$.
• "3 less than twice the number" can be written as $2𝑥-3$.

According to the problem, these two expressions are equal: $𝑥+3=2𝑥-3$

We will solve this equation step-by-step:

1. Subtract $𝑥$ from both sides of the equation:

$$\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">-</span>\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}<span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}<span\; style="font-size:\; x-large;">-</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">-</span>\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}$$

This simplifies to:

$$\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}<span\; style="font-size:\; x-large;">-</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}$$

2. Add 3 to both sides of the equation:

$$\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}<span\; style="font-size:\; x-large;">-</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}$$

This simplifies to:

$$\mathrm{<span\; style="font-size:\; x-large;">6</span>}<span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">𝑥</span>}$$

Thus, the number is $𝑥=6$.

To verify the solution, substitute $𝑥=6$ back into the original condition:

• Increased by 3: $6+3=9$
• 3 less than twice the number: $2\times 6-3=12-3=9$

Since both expressions are equal, the solution $𝑥=6$ is correct.

Therefore, the number is $\boxed{{\displaystyle 6}}$.