Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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