Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+4}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4+3x } & = & 13 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &4x & = &9\\\Leftrightarrow & \color{red}{4}x & = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-6}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-6x } & = & -6 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & 13x \color{blue}{-6x } & = & -6 \color{blue}{+6} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x } & = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -12 \color{blue}{+10} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+15}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & 13 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 13 \color{blue}{-15} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x } & = & -10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &-9x & = &2\\\Leftrightarrow & \color{red}{-9}x & = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+5}& = & 3 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-7x } & = & 3 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -9x \color{blue}{-7x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-16x & = &-2\\\Leftrightarrow & \color{red}{-16}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+12}& = & 3 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+6x } & = & 3 \color{red}{ -6x }\color{blue}{-12+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+9}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9+13x } & = & -15 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -15 \color{blue}{-9} \\\Leftrightarrow &23x & = &-24\\\Leftrightarrow & \color{red}{23}x & = &-24\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-24}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{23} } & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+4}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-11x } & = & 12 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &x & = &8\\\Leftrightarrow & \color{red}{}x & = &8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 8 \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-12}& = & -12 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-9x } & = & -12 \color{red}{ +9x }\color{blue}{+12-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & -12 \color{blue}{+12} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+11}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-11x } & = & 3 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 8x \color{blue}{-11x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5-x } & = & 1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)