Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+5}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-13x } & = & 3 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 3 \color{blue}{-5} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-7}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7+11x } & = & -10 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &17x & = &-3\\\Leftrightarrow & \color{red}{17}x & = &-3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-14x & = &30\\\Leftrightarrow & \color{red}{-14}x & = &30\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{30}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+9}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-7x } & = & -4 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -4 \color{blue}{-9} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+2}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x } & = & 11 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 11 \color{blue}{-2} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15-x } & = & 8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-15} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{-9}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9-13x } & = & -10 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -6x \color{blue}{-13x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x } & = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &-3x & = &6\\\Leftrightarrow & \color{red}{-3}x & = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-12}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-3x } & = & -6 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -6 \color{blue}{+12} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-2}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-3x } & = & -9 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 14x \color{blue}{-3x } & = & -9 \color{blue}{+2} \\\Leftrightarrow &11x & = &-7\\\Leftrightarrow & \color{red}{11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-2}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2-13x } & = & -7 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -7 \color{blue}{+2} \\\Leftrightarrow &-16x & = &-5\\\Leftrightarrow & \color{red}{-16}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{16} } & & \\ & V = \left\{ \frac{5}{16} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+9}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & 6 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)