Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6-x } & = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+3}& = & 13 \color{red}{ +8x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-8x } & = & 13 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & 15x \color{blue}{-8x } & = & 13 \color{blue}{-3} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{+1}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x } & = & -2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -2 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-3\\\Leftrightarrow & \color{red}{-9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+9}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-11x } & = & -2 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & -2 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-11\\\Leftrightarrow & \color{red}{-5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-13}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-3x } & = & -2 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -2 \color{blue}{+13} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+4}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-7x } & = & -5 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -5 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-9\\\Leftrightarrow & \color{red}{-17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-9}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+4}& = & 8 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4-3x } & = & 8 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & -x \color{blue}{-3x } & = & 8 \color{blue}{-4} \\\Leftrightarrow &-4x & = &4\\\Leftrightarrow & \color{red}{-4}x & = &4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{4}{-4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+2}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2+11x } & = & 2 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 2 \color{blue}{-2} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &x & = &-27\\\Leftrightarrow & \color{red}{}x & = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-1}& = & -5 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1-12x } & = & -5 \color{red}{ +12x }\color{blue}{+1-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -5 \color{blue}{+1} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{-9}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9-x } & = & 10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+9}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & -13 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-22\\\Leftrightarrow & \color{red}{-5}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)