Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-2}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2-11x } & = & 12 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-3x & = &14\\\Leftrightarrow & \color{red}{-3}x & = &14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+9}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9-6x } & = & 12 \color{red}{ +6x }\color{blue}{-9-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+3}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-3x } & = & -6 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -6 \color{blue}{-3} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+6}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6-7x } & = & 7 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-3x & = &1\\\Leftrightarrow & \color{red}{-3}x & = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+15}& = & 15 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-11x } & = & 15 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-21x & = &0\\\Leftrightarrow & \color{red}{-21}x & = &0\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{0}{-21} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-4}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & 5x \color{red}{-4}\color{blue}{+4-7x } & = & 10 \color{red}{ +7x }\color{blue}{+4-7x } \\\Leftrightarrow & 5x \color{blue}{-7x } & = & 10 \color{blue}{+4} \\\Leftrightarrow &-2x & = &14\\\Leftrightarrow & \color{red}{-2}x & = &14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{14}{-2} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-12}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x } & = & 13 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 13 \color{blue}{+12} \\\Leftrightarrow &-28x & = &25\\\Leftrightarrow & \color{red}{-28}x & = &25\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{25}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{28} } & & \\ & V = \left\{ \frac{-25}{28} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-3}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+2x } & = & 11 \color{red}{ -2x }\color{blue}{+3+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+9}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9-5x } & = & 4 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 2x \color{blue}{-5x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-8}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-x } & = & 1 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{+8} \\\Leftrightarrow &-11x & = &9\\\Leftrightarrow & \color{red}{-11}x & = &9\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{9}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-6}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6+13x } & = & 8 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &12x & = &14\\\Leftrightarrow & \color{red}{12}x & = &14\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{14}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)