Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{-6}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6+14x } & = & 2 \color{red}{ -14x }\color{blue}{+6+14x } \\\Leftrightarrow & x \color{blue}{+14x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &15x & = &8\\\Leftrightarrow & \color{red}{15}x & = &8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-5}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5+11x } & = & -7 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -7 \color{blue}{+5} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+11}& = & -10 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-11x } & = & -10 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-x & = &-21\\\Leftrightarrow & \color{red}{-}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-21}{-1} \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-7}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-7}\color{blue}{+7-3x } & = & -1 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 7 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10-x } & = & -11 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -11 \color{blue}{-10} \\\Leftrightarrow &-8x & = &-21\\\Leftrightarrow & \color{red}{-8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-15}& = & -10 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15+8x } & = & -10 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 9x \color{blue}{+8x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-8}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8+11x } & = & 2 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &17x & = &10\\\Leftrightarrow & \color{red}{17}x & = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+3}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-11x } & = & 5 \color{red}{ +11x }\color{blue}{-3-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 4 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-4}& = & -8 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+15x } & = & -8 \color{red}{ -15x }\color{blue}{+4+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -8 \color{blue}{+4} \\\Leftrightarrow &19x & = &-4\\\Leftrightarrow & \color{red}{19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-11}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-4x } & = & 3 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-x & = &14\\\Leftrightarrow & \color{red}{-}x & = &14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{14}{-1} \\\Leftrightarrow & \color{green}{ x = -14 } & & \\ & V = \left\{ -14 \right\} & \\\end{align}\)