Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-5}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & -8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{+5} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{-10}& = & -14 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-10}\color{blue}{+10+3x } & = & -14 \color{red}{ -3x }\color{blue}{+10+3x } \\\Leftrightarrow & 7x \color{blue}{+3x } & = & -14 \color{blue}{+10} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+1}& = & -8 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+7x } & = & -8 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-7}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-8x } & = & -9 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & 11x \color{blue}{-8x } & = & -9 \color{blue}{+7} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+5}& = & 15 \color{red}{ -2x } \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5+2x } & = & 15 \color{red}{ -2x }\color{blue}{-5+2x } \\\Leftrightarrow & 13x \color{blue}{+2x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &15x & = &10\\\Leftrightarrow & \color{red}{15}x & = &10\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{10}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 2x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x } & = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &x & = &24\\\Leftrightarrow & \color{red}{}x & = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{+14}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-7x } & = & -8 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -8 \color{blue}{-14} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+1}& = & 6 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-6x } & = & 6 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & 5x \color{blue}{-6x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-6}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & -15 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+3}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-14x } & = & 14 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 14 \color{blue}{-3} \\\Leftrightarrow &-27x & = &11\\\Leftrightarrow & \color{red}{-27}x & = &11\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{11}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{27} } & & \\ & V = \left\{ \frac{-11}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-10}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10-13x } & = & -5 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 6x \color{blue}{-13x } & = & -5 \color{blue}{+10} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+7}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-x } & = & -15 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &-8x & = &-22\\\Leftrightarrow & \color{red}{-8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)