Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+10}& = & 12 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-5x } & = & 12 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 11x \color{blue}{-5x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &6x & = &2\\\Leftrightarrow & \color{red}{6}x & = &2\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{2}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-6}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-7x } & = & -5 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-20x & = &1\\\Leftrightarrow & \color{red}{-20}x & = &1\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{1}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{20} } & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+15}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-7x } & = & 2 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 2 \color{blue}{-15} \\\Leftrightarrow &-20x & = &-13\\\Leftrightarrow & \color{red}{-20}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-13}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{13}{20} } & & \\ & V = \left\{ \frac{13}{20} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+9}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-7x } & = & 4 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 6x \color{blue}{-7x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-x & = &-5\\\Leftrightarrow & \color{red}{-}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-3}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-7x } & = & -9 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &-17x & = &-6\\\Leftrightarrow & \color{red}{-17}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-x } & = & 11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &6x & = &6\\\Leftrightarrow & \color{red}{6}x & = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+10}& = & 12 \color{red}{ +15x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10-15x } & = & 12 \color{red}{ +15x }\color{blue}{-10-15x } \\\Leftrightarrow & -x \color{blue}{-15x } & = & 12 \color{blue}{-10} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & 14 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 14 \color{blue}{-9} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & -14 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-25\\\Leftrightarrow & \color{red}{-3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-9}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-x } & = & -6 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-6}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+2x } & = & -15 \color{red}{ -2x }\color{blue}{+6+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & -15 \color{blue}{+6} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)