Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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