Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+7}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-7x } & = & -12 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -12 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-19\\\Leftrightarrow & \color{red}{-13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-19}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{19}{13} } & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-x } & = & 4 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 4 \color{blue}{+10} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x } & = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-13x & = &-2\\\Leftrightarrow & \color{red}{-13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-x } & = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 6 \color{blue}{+6} \\\Leftrightarrow &12x & = &12\\\Leftrightarrow & \color{red}{12}x & = &12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{12}{12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{-15}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-15}\color{blue}{+15-10x } & = & -12 \color{red}{ +10x }\color{blue}{+15-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+7}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+7}\color{blue}{-7-11x } & = & 10 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-6x & = &3\\\Leftrightarrow & \color{red}{-6}x & = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+9}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9+13x } & = & 8 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &27x & = &-1\\\Leftrightarrow & \color{red}{27}x & = &-1\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-1}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{27} } & & \\ & V = \left\{ \frac{-1}{27} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-6}& = & 7 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6-13x } & = & 7 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 9x \color{blue}{-13x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+13}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-x } & = & 1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 1 \color{blue}{-13} \\\Leftrightarrow &14x & = &-12\\\Leftrightarrow & \color{red}{14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-8}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+13x } & = & -5 \color{red}{ -13x }\color{blue}{+8+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -5 \color{blue}{+8} \\\Leftrightarrow &23x & = &3\\\Leftrightarrow & \color{red}{23}x & = &3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{3}{23} } & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+10}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x } & = & -8 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -8 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-18\\\Leftrightarrow & \color{red}{-9}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-18}{-9} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 4x \color{red}{-3}& = & 9 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3-9x } & = & 9 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 9 \color{blue}{+3} \\\Leftrightarrow &-5x & = &12\\\Leftrightarrow & \color{red}{-5}x & = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)