Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 3x \color{red}{+8}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-7x } & = & -15 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -15 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-23\\\Leftrightarrow & \color{red}{-4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-23}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{23}{4} } & & \\ & V = \left\{ \frac{23}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-1}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+5x } & = & -13 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -13 \color{blue}{+1} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15-x } & = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &9x & = &16\\\Leftrightarrow & \color{red}{9}x & = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+3}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+11x } & = & 4 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & 4 \color{blue}{-3} \\\Leftrightarrow &17x & = &1\\\Leftrightarrow & \color{red}{17}x & = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-2}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-2}\color{blue}{+2-13x } & = & 5 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 5 \color{blue}{+2} \\\Leftrightarrow &-17x & = &7\\\Leftrightarrow & \color{red}{-17}x & = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-5}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x } & = & 12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 12 \color{blue}{+5} \\\Leftrightarrow &-10x & = &17\\\Leftrightarrow & \color{red}{-10}x & = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+4}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4+5x } & = & 2 \color{red}{ -5x }\color{blue}{-4+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{+12}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12-5x } & = & -8 \color{red}{ +5x }\color{blue}{-12-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &9x & = &-20\\\Leftrightarrow & \color{red}{9}x & = &-20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-4}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & 1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-13}& = & -8 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13+13x } & = & -8 \color{red}{ -13x }\color{blue}{+13+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &23x & = &5\\\Leftrightarrow & \color{red}{23}x & = &5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{5}{23} } & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-1}& = & 11 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1+5x } & = & 11 \color{red}{ -5x }\color{blue}{+1+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &13x & = &12\\\Leftrightarrow & \color{red}{13}x & = &12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -2 \color{blue}{+6} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)