Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-8}& = & -2 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+6x } & = & -2 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &19x & = &6\\\Leftrightarrow & \color{red}{19}x & = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-5}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-13x } & = & 4 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &-28x & = &9\\\Leftrightarrow & \color{red}{-28}x & = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{+5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x } & = & 7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 7 \color{blue}{-5} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+13}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13+2x } & = & 9 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & 8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-15x & = &2\\\Leftrightarrow & \color{red}{-15}x & = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-3}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-4x } & = & 3 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-x } & = & 11 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 11 \color{blue}{+7} \\\Leftrightarrow &10x & = &18\\\Leftrightarrow & \color{red}{10}x & = &18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+4}& = & 7 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x } & = & 7 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &19x & = &3\\\Leftrightarrow & \color{red}{19}x & = &3\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{3}{19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x } & = & 9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 9 \color{blue}{-12} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-10}& = & 7 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-2x } & = & 7 \color{red}{ +2x }\color{blue}{+10-2x } \\\Leftrightarrow & 3x \color{blue}{-2x } & = & 7 \color{blue}{+10} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-3}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-8x } & = & 10 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &-x & = &13\\\Leftrightarrow & \color{red}{-}x & = &13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{13}{-1} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)