Hi student, let me help you out!
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First of all, let the number be z.
Now, since the question says "4 times a number", we should multiply 4 times the number z: [tex]\mathsf{4z}[/tex].
Now, this little expression equals 84 less than 6 times the number (which is z). The phrase "84 less than" tells us to subtract 84 from 6 times z: [tex]\mathsf{6z-84}[/tex].
Put this together and obtain ✨ [tex]\bigstar\underline{\boxed{\mathrm{4z=6z-84}}}[/tex].
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Now let's solve the equation for z by following several steps, which are:
Step 1. Subtract 6z from both sides: [tex]\mathsf{4z-6z=6z-6z-84}[/tex].
Upon simplifying, we obtain [tex]\mathsf{-2z=-84}[/tex]
Step 2. Solve for z by dividing both sides by -2: [tex]\mathsf{-2z\div(-2)=-84\div(-2)}[/tex].
Upon simplifying, we obtain ✨ [tex]\bigstar\underline{\boxed{\mathrm{z=42}}}[/tex].
Hope this helped you out, ask in comments if any queries arise.
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The number which is Four times a number is 84 less than 6 times the number will be 42.
When trying to set up or construct a linear equation to fit a real-world application, identify the known quantities and treat the unknown quantity as a variable.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let the number be x
Four times = 4x
84 less than 6 times the number = 6x - 84
Both are equal according to the question
4x = 6x - 84
4x - 6x = -84
-2x = - 84
x = 84/2 = 42 hence, that number will be 42.
For more about the equation
brainly.com/question/2263981
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