Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(14x+11=7+9x\)
2. \(-6x+7=1+x\)
3. \(-7x-6=-3+x\)
4. \(13x+12=-9+12x\)
5. \(4x+2=-8-15x\)
6. \(-x+3=2+7x\)
7. \(14x-4=-8+9x\)
8. \(-11x+4=7+12x\)
9. \(14x+1=5+x\)
10. \(-3x-9=8+x\)
11. \(8x-15=10+11x\)
12. \(-x-6=-8+2x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+11}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-9x } & = & 7 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 7 \color{blue}{-11} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-x } & = & 1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 1 \color{blue}{-7} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+12}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12-12x } & = & -9 \color{red}{ +12x }\color{blue}{-12-12x } \\\Leftrightarrow & 13x \color{blue}{-12x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &x & = &-21\\\Leftrightarrow & \color{red}{}x & = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+2}& = & -8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+15x } & = & -8 \color{red}{ -15x }\color{blue}{-2+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -8 \color{blue}{-2} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+3}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3-7x } & = & 2 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 2 \color{blue}{-3} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-4}& = & -8 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-9x } & = & -8 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &5x & = &-4\\\Leftrightarrow & \color{red}{5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+4}& = & 7 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-12x } & = & 7 \color{red}{ +12x }\color{blue}{-4-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-23x & = &3\\\Leftrightarrow & \color{red}{-23}x & = &3\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{3}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &13x & = &4\\\Leftrightarrow & \color{red}{13}x & = &4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-x } & = & 8 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{+9} \\\Leftrightarrow &-4x & = &17\\\Leftrightarrow & \color{red}{-4}x & = &17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-15}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15-11x } & = & 10 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 10 \color{blue}{+15} \\\Leftrightarrow &-3x & = &25\\\Leftrightarrow & \color{red}{-3}x & = &25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-6}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6-2x } & = & -8 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & -x \color{blue}{-2x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)