Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-2}& = & -13 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2+7x } & = & -13 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 5x \color{blue}{+7x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &12x & = &-11\\\Leftrightarrow & \color{red}{12}x & = &-11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{12} } & & \\ & V = \left\{ \frac{-11}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+1}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-3x } & = & 14 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & 14 \color{blue}{-1} \\\Leftrightarrow &x & = &13\\\Leftrightarrow & \color{red}{}x & = &13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 13 \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-3}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x } & = & -4 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{+3} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+15}& = & -12 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-14x } & = & -12 \color{red}{ +14x }\color{blue}{-15-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -12 \color{blue}{-15} \\\Leftrightarrow &-23x & = &-27\\\Leftrightarrow & \color{red}{-23}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-27}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{27}{23} } & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{-13}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+7x } & = & -4 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 11x \color{blue}{+7x } & = & -4 \color{blue}{+13} \\\Leftrightarrow &18x & = &9\\\Leftrightarrow & \color{red}{18}x & = &9\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{9}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+8}& = & -5 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8-14x } & = & -5 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -5 \color{blue}{-8} \\\Leftrightarrow &-27x & = &-13\\\Leftrightarrow & \color{red}{-27}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-13}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{13}{27} } & & \\ & V = \left\{ \frac{13}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+8}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-5x } & = & 14 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+13}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+13}\color{blue}{-13+13x } & = & 4 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &20x & = &-9\\\Leftrightarrow & \color{red}{20}x & = &-9\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-9}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{20} } & & \\ & V = \left\{ \frac{-9}{20} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-8}\color{blue}{+8-x } & = & -2 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -2 \color{blue}{+8} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-7}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-9x } & = & -15 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-10}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-7x } & = & -7 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)