Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-4}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-4x } & = & -1 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+7}& = & -1 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+9x } & = & -1 \color{red}{ -9x }\color{blue}{-7+9x } \\\Leftrightarrow & 7x \color{blue}{+9x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &16x & = &-8\\\Leftrightarrow & \color{red}{16}x & = &-8\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-8}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-9}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-14x } & = & -14 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &-23x & = &-5\\\Leftrightarrow & \color{red}{-23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-5}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-13}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-4x } & = & -14 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -14 \color{blue}{+13} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-6}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-9x } & = & 7 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & 14x \color{blue}{-9x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-12}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12-7x } & = & 10 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & x \color{blue}{-7x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-6x & = &22\\\Leftrightarrow & \color{red}{-6}x & = &22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & -5 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-14\\\Leftrightarrow & \color{red}{-14}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+8}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8-12x } & = & -12 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & -12 \color{blue}{-8} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7-x } & = & 3 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+10}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+2x } & = & 8 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 8 \color{blue}{-10} \\\Leftrightarrow &7x & = &-2\\\Leftrightarrow & \color{red}{7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-11}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-8x } & = & 13 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &-23x & = &24\\\Leftrightarrow & \color{red}{-23}x & = &24\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{24}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{23} } & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)