Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+12}& = & 8 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-6x } & = & 8 \color{red}{ +6x }\color{blue}{-12-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x } & = & 13 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{-10} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{-7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x } & = & -13 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-x } & = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-5}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-11x } & = & 8 \color{red}{ +11x }\color{blue}{+5-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 8 \color{blue}{+5} \\\Leftrightarrow &-7x & = &13\\\Leftrightarrow & \color{red}{-7}x & = &13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-9}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9-13x } & = & -5 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 10x \color{blue}{-13x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 7x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-15}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-15}\color{blue}{+15-7x } & = & -1 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{+15} \\\Leftrightarrow &-13x & = &14\\\Leftrightarrow & \color{red}{-13}x & = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-8}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-8}\color{blue}{+8+6x } & = & 12 \color{red}{ -6x }\color{blue}{+8+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & 12 \color{blue}{+8} \\\Leftrightarrow &13x & = &20\\\Leftrightarrow & \color{red}{13}x & = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-12}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12-x } & = & 3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 3 \color{blue}{+12} \\\Leftrightarrow &5x & = &15\\\Leftrightarrow & \color{red}{5}x & = &15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{15}{5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+13}& = & 13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+5x } & = & 13 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+8}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8-8x } & = & -2 \color{red}{ +8x }\color{blue}{-8-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)