Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-15}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15+7x } & = & -13 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -13 \color{blue}{+15} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+1}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-x } & = & -7 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-1} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-x } & = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-11}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x } & = & -3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+15}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15+8x } & = & -3 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & -x \color{blue}{+8x } & = & -3 \color{blue}{-15} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+2}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2-x } & = & -2 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{-2} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+6}& = & -14 \color{red}{ -2x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+2x } & = & -14 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 9x \color{blue}{+2x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-9}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-2x } & = & -12 \color{red}{ +2x }\color{blue}{+9-2x } \\\Leftrightarrow & 9x \color{blue}{-2x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-5}& = & 14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+6x } & = & 14 \color{red}{ -6x }\color{blue}{+5+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+7}& = & -14 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7+15x } & = & -14 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -14 \color{blue}{-7} \\\Leftrightarrow &23x & = &-21\\\Leftrightarrow & \color{red}{23}x & = &-21\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-21}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{23} } & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-11}& = & -2 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+5x } & = & -2 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)