Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+3}& = & -11 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-9x } & = & -11 \color{red}{ +9x }\color{blue}{-3-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-x } & = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+5}& = & -11 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5-4x } & = & -11 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -11 \color{blue}{-5} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+11}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11+3x } & = & -2 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -2 \color{blue}{-11} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-x } & = & 4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-11}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-3x } & = & -8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -8 \color{blue}{+11} \\\Leftrightarrow &11x & = &3\\\Leftrightarrow & \color{red}{11}x & = &3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+9}& = & -13 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9+6x } & = & -13 \color{red}{ -6x }\color{blue}{-9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &19x & = &-22\\\Leftrightarrow & \color{red}{19}x & = &-22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{19} } & & \\ & V = \left\{ \frac{-22}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-4}& = & -8 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4+2x } & = & -8 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+5}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5+7x } & = & 15 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 15 \color{blue}{-5} \\\Leftrightarrow &19x & = &10\\\Leftrightarrow & \color{red}{19}x & = &10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{10}{19} } & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+8}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-9x } & = & 4 \color{red}{ +9x }\color{blue}{-8-9x } \\\Leftrightarrow & -13x \color{blue}{-9x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &-22x & = &-4\\\Leftrightarrow & \color{red}{-22}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-4}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+9}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-7x } & = & -13 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &x & = &-22\\\Leftrightarrow & \color{red}{}x & = &-22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -22 \\\Leftrightarrow & \color{green}{ x = -22 } & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+11}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & -10 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)