Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+12}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-9x } & = & -10 \color{red}{ +9x }\color{blue}{-12-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &-20x & = &-22\\\Leftrightarrow & \color{red}{-20}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-22}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+10}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+11x } & = & -4 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &17x & = &-14\\\Leftrightarrow & \color{red}{17}x & = &-14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{17} } & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+7}& = & -6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+15x } & = & -6 \color{red}{ -15x }\color{blue}{-7+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &19x & = &-13\\\Leftrightarrow & \color{red}{19}x & = &-13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{19} } & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+8}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & -4 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+3}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3+11x } & = & 6 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & -x \color{blue}{+11x } & = & 6 \color{blue}{-3} \\\Leftrightarrow &10x & = &3\\\Leftrightarrow & \color{red}{10}x & = &3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+12}& = & 3 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12+15x } & = & 3 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & 3 \color{blue}{-12} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+12}& = & -3 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+15x } & = & -3 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -3 \color{blue}{-12} \\\Leftrightarrow &23x & = &-15\\\Leftrightarrow & \color{red}{23}x & = &-15\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-15}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{23} } & & \\ & V = \left\{ \frac{-15}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+9}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-13x } & = & -6 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -6 \color{blue}{-9} \\\Leftrightarrow &-28x & = &-15\\\Leftrightarrow & \color{red}{-28}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{-15}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{15}{28} } & & \\ & V = \left\{ \frac{15}{28} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-13}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13-7x } & = & -8 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{+10}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+11x } & = & 15 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 15 \color{blue}{-10} \\\Leftrightarrow &17x & = &5\\\Leftrightarrow & \color{red}{17}x & = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-14}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14+7x } & = & 14 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &15x & = &28\\\Leftrightarrow & \color{red}{15}x & = &28\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{28}{15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)