High School

1. Three less than a number.
2. Four more than a number is eleven.
3. The product of three and a number.
4. Eight more than double a number is nine.
5. A number divided by seven is two.
6. The product of a number and six is eighteen.

Answer :

Let's solve the questions step-by-step:

  1. Three less than a number.

    Let the number be [tex]x[/tex]. Three less than this number means [tex]x - 3[/tex].

  2. Four more than a number is eleven.

    Again, let the number be [tex]x[/tex]. The equation for this statement is:

    [tex]x + 4 = 11[/tex]

    To find [tex]x[/tex], subtract 4 from both sides:

    [tex]x = 11 - 4[/tex]
    [tex]x = 7[/tex]

  3. The product of three and a number.

    Let the number be [tex]x[/tex]. The product of three and this number is [tex]3x[/tex].

  4. Eight more than double a number is nine.

    Let the number be [tex]x[/tex]. The equation for this is:

    [tex]2x + 8 = 9[/tex]

    Subtract 8 from both sides:

    [tex]2x = 9 - 8[/tex]
    [tex]2x = 1[/tex]

    Divide both sides by 2 to find [tex]x[/tex]:

    [tex]x = \frac{1}{2}[/tex]

  5. A number divided by seven is two.

    Let the number be [tex]x[/tex]. The equation is:

    [tex]\frac{x}{7} = 2[/tex]

    Multiply both sides by 7 to find [tex]x[/tex]:

    [tex]x = 2 \times 7[/tex]
    [tex]x = 14[/tex]

  6. The product of a number and six is eighteen.

    Let the number be [tex]x[/tex]. The equation is:

    [tex]6x = 18[/tex]

    Divide both sides by 6 to find [tex]x[/tex]:

    [tex]x = \frac{18}{6}[/tex]
    [tex]x = 3[/tex]

These solutions help students understand how to translate word problems into algebraic expressions and equations, and then solve them to find the unknown values.

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