Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+6}& = & 13 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6+9x } & = & 13 \color{red}{ -9x }\color{blue}{-6+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x } & = & -3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -3 \color{blue}{+6} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+5}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5+11x } & = & 8 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 8 \color{blue}{-5} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-11}\color{blue}{+11-x } & = & -13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+11} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-11}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11-11x } & = & -3 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &-x & = &8\\\Leftrightarrow & \color{red}{-}x & = &8\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{8}{-1} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{+11}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-5x } & = & 6 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &9x & = &-5\\\Leftrightarrow & \color{red}{9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+13}& = & 8 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13+6x } & = & 8 \color{red}{ -6x }\color{blue}{-13+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-8\\\Leftrightarrow & \color{red}{-5}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x } & = & 6 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{+7} \\\Leftrightarrow &-11x & = &13\\\Leftrightarrow & \color{red}{-11}x & = &13\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{13}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-11}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11-x } & = & 12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 12 \color{blue}{+11} \\\Leftrightarrow &9x & = &23\\\Leftrightarrow & \color{red}{9}x & = &23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-15}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-7x } & = & -10 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-20x & = &5\\\Leftrightarrow & \color{red}{-20}x & = &5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+8}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8-11x } & = & 12 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 12 \color{blue}{-8} \\\Leftrightarrow &-5x & = &4\\\Leftrightarrow & \color{red}{-5}x & = &4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)