Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-x } & = & -12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x } & = & -14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-22\\\Leftrightarrow & \color{red}{-7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{-14}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-14}\color{blue}{+14-4x } & = & -14 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+10}& = & 3 \color{red}{ +6x } \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10-6x } & = & 3 \color{red}{ +6x }\color{blue}{-10-6x } \\\Leftrightarrow & 7x \color{blue}{-6x } & = & 3 \color{blue}{-10} \\\Leftrightarrow &x & = &-7\\\Leftrightarrow & \color{red}{}x & = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-9}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+7x } & = & -1 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &19x & = &8\\\Leftrightarrow & \color{red}{19}x & = &8\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{8}{19} \\\Leftrightarrow & \color{green}{ x = \frac{8}{19} } & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-2}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-5x } & = & 13 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &-17x & = &15\\\Leftrightarrow & \color{red}{-17}x & = &15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+1}& = & -8 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+5x } & = & -8 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -8 \color{blue}{-1} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{+6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 13 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 13 \color{blue}{-6} \\\Leftrightarrow &-6x & = &7\\\Leftrightarrow & \color{red}{-6}x & = &7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{+15}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x } & = & -5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -5 \color{blue}{-15} \\\Leftrightarrow &-14x & = &-20\\\Leftrightarrow & \color{red}{-14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 2x \color{red}{+2}& = & 7 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-9x } & = & 7 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & 2x \color{blue}{-9x } & = & 7 \color{blue}{-2} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-9}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-13x } & = & -14 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & -14 \color{blue}{+9} \\\Leftrightarrow &-15x & = &-5\\\Leftrightarrow & \color{red}{-15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-x } & = & -1 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -1 \color{blue}{-1} \\\Leftrightarrow &-3x & = &-2\\\Leftrightarrow & \color{red}{-3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)