Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 5x \color{red}{-15}& = & -15 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+14x } & = & -15 \color{red}{ -14x }\color{blue}{+15+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &19x & = &0\\\Leftrightarrow & \color{red}{19}x & = &0\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{0}{19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-7}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-13x } & = & -2 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-2x & = &5\\\Leftrightarrow & \color{red}{-2}x & = &5\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{5}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = & -13 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+13x } & = & -13 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & -13 \color{blue}{+2} \\\Leftrightarrow &20x & = &-11\\\Leftrightarrow & \color{red}{20}x & = &-11\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-11}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{20} } & & \\ & V = \left\{ \frac{-11}{20} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+5}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+5}\color{blue}{-5-3x } & = & 11 \color{red}{ +3x }\color{blue}{-5-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-8}& = & -4 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8-9x } & = & -4 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &-13x & = &4\\\Leftrightarrow & \color{red}{-13}x & = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-9}& = & 14 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-14x } & = & 14 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &-27x & = &23\\\Leftrightarrow & \color{red}{-27}x & = &23\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{23}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{27} } & & \\ & V = \left\{ \frac{-23}{27} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-10}& = & 13 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x } & = & 13 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & 13 \color{blue}{+10} \\\Leftrightarrow &-25x & = &23\\\Leftrightarrow & \color{red}{-25}x & = &23\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{23}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+12}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12+11x } & = & 5 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 5 \color{blue}{-12} \\\Leftrightarrow &23x & = &-7\\\Leftrightarrow & \color{red}{23}x & = &-7\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-7}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{23} } & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+15}& = & 11 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15+7x } & = & 11 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 11 \color{blue}{-15} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{-1}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-7x } & = & -2 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 2x \color{blue}{-7x } & = & -2 \color{blue}{+1} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+11}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-x } & = & -11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{-11} \\\Leftrightarrow &-6x & = &-22\\\Leftrightarrow & \color{red}{-6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-22}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{+12}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & 8 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)