Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+7}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-7x } & = & 6 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-10x & = &-1\\\Leftrightarrow & \color{red}{-10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+13}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-5x } & = & 14 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & 9x \color{blue}{-5x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+10}& = & -12 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10+15x } & = & -12 \color{red}{ -15x }\color{blue}{-10+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & -12 \color{blue}{-10} \\\Leftrightarrow &23x & = &-22\\\Leftrightarrow & \color{red}{23}x & = &-22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{23} } & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+11}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+11}\color{blue}{-11-x } & = & 5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 5 \color{blue}{-11} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-5}& = & 1 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x } & = & 1 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &-17x & = &6\\\Leftrightarrow & \color{red}{-17}x & = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-x } & = & -3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -3 \color{blue}{-4} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+12}& = & 12 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+10x } & = & 12 \color{red}{ -10x }\color{blue}{-12+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 12 \color{blue}{-12} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-5}& = & -11 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5+4x } & = & -11 \color{red}{ -4x }\color{blue}{+5+4x } \\\Leftrightarrow & 5x \color{blue}{+4x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &9x & = &-6\\\Leftrightarrow & \color{red}{9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-6}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+7}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+7}\color{blue}{-7+13x } & = & 10 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &27x & = &3\\\Leftrightarrow & \color{red}{27}x & = &3\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{3}{27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-x } & = & -2 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-2}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x } & = & 9 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 9 \color{blue}{+2} \\\Leftrightarrow &-15x & = &11\\\Leftrightarrow & \color{red}{-15}x & = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x } & = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)