Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+4}& = & 7 \color{red}{ +6x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4-6x } & = & 7 \color{red}{ +6x }\color{blue}{-4-6x } \\\Leftrightarrow & -x \color{blue}{-6x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-4}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-5x } & = & -13 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+10}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10-14x } & = & -12 \color{red}{ +14x }\color{blue}{-10-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-1}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-13x } & = & -7 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -7 \color{blue}{+1} \\\Leftrightarrow &-19x & = &-6\\\Leftrightarrow & \color{red}{-19}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-6}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{+2}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-13x } & = & -6 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &-28x & = &-8\\\Leftrightarrow & \color{red}{-28}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-8}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+11}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+11x } & = & -14 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &15x & = &-25\\\Leftrightarrow & \color{red}{15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8-x } & = & -14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-x } & = & 10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &5x & = &22\\\Leftrightarrow & \color{red}{5}x & = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 6x \color{red}{-15}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15+11x } & = & 12 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 12 \color{blue}{+15} \\\Leftrightarrow &17x & = &27\\\Leftrightarrow & \color{red}{17}x & = &27\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{27}{17} \\\Leftrightarrow & \color{green}{ x = \frac{27}{17} } & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-1}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-1}\color{blue}{+1-x } & = & 3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+2}& = & -6 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+6x } & = & -6 \color{red}{ -6x }\color{blue}{-2+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -6 \color{blue}{-2} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-x } & = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)