Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+2}\color{blue}{-2-x } & = & 8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14-x } & = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 2 \color{blue}{+14} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-5}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5-5x } & = & -3 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-10}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-13x } & = & 5 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+11}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11+12x } & = & -15 \color{red}{ -12x }\color{blue}{-11+12x } \\\Leftrightarrow & -x \color{blue}{+12x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &11x & = &-26\\\Leftrightarrow & \color{red}{11}x & = &-26\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-26}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{11} } & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{-15}& = & -10 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-6x } & = & -10 \color{red}{ +6x }\color{blue}{+15-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -10 \color{blue}{+15} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+8}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8-5x } & = & -14 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & x \color{blue}{-5x } & = & -14 \color{blue}{-8} \\\Leftrightarrow &-4x & = &-22\\\Leftrightarrow & \color{red}{-4}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-12}& = & -4 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+15x } & = & -4 \color{red}{ -15x }\color{blue}{+12+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & -4 \color{blue}{+12} \\\Leftrightarrow &28x & = &8\\\Leftrightarrow & \color{red}{28}x & = &8\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{8}{28} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+5}& = & -5 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+14x } & = & -5 \color{red}{ -14x }\color{blue}{-5+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -5 \color{blue}{-5} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-10}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-7x } & = & -15 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-17x & = &-5\\\Leftrightarrow & \color{red}{-17}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-5}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-1}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x } & = & 11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)