Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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