Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & 1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 1 \color{blue}{+10} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+8}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+8x } & = & 6 \color{red}{ -8x }\color{blue}{-8+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &19x & = &-2\\\Leftrightarrow & \color{red}{19}x & = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-x } & = & -13 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -13 \color{blue}{+8} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+4}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & 12 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+13}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13+2x } & = & 9 \color{red}{ -2x }\color{blue}{-13+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 9 \color{blue}{-13} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{-6}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & 12 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 12 \color{blue}{+6} \\\Leftrightarrow &-15x & = &18\\\Leftrightarrow & \color{red}{-15}x & = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+14}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-14x } & = & 11 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 11 \color{blue}{-14} \\\Leftrightarrow &-27x & = &-3\\\Leftrightarrow & \color{red}{-27}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-3}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-9}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-11x } & = & -5 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & -2x \color{blue}{-11x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 9 \color{blue}{-7} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-12}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-11x } & = & -7 \color{red}{ +11x }\color{blue}{+12-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+10}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-5x } & = & 13 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 4x \color{blue}{-5x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-x & = &3\\\Leftrightarrow & \color{red}{-}x & = &3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{3}{-1} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{-9}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-9x } & = & 3 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 3 \color{blue}{+9} \\\Leftrightarrow &-17x & = &12\\\Leftrightarrow & \color{red}{-17}x & = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)