Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-x } & = & 11 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 11 \color{blue}{-6} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-x } & = & 5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-x } & = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-6x & = &24\\\Leftrightarrow & \color{red}{-6}x & = &24\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{24}{-6} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x } & = & 14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 14 \color{blue}{+14} \\\Leftrightarrow &-3x & = &28\\\Leftrightarrow & \color{red}{-3}x & = &28\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{28}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{3} } & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+4}& = & 12 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4+3x } & = & 12 \color{red}{ -3x }\color{blue}{-4+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 12 \color{blue}{-4} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-x } & = & 13 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+15}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15-5x } & = & -10 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & -10 \color{blue}{-15} \\\Leftrightarrow &3x & = &-25\\\Leftrightarrow & \color{red}{3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{3} } & & \\ & V = \left\{ \frac{-25}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{-1}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-5x } & = & -3 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -x \color{blue}{-5x } & = & -3 \color{blue}{+1} \\\Leftrightarrow &-6x & = &-2\\\Leftrightarrow & \color{red}{-6}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-13}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-13}\color{blue}{+13+7x } & = & 2 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 2 \color{blue}{+13} \\\Leftrightarrow &19x & = &15\\\Leftrightarrow & \color{red}{19}x & = &15\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{15}{19} \\\Leftrightarrow & \color{green}{ x = \frac{15}{19} } & & \\ & V = \left\{ \frac{15}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-2}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+10x } & = & 15 \color{red}{ -10x }\color{blue}{+2+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &21x & = &17\\\Leftrightarrow & \color{red}{21}x & = &17\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{17}{21} \\\Leftrightarrow & \color{green}{ x = \frac{17}{21} } & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-9}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-14x } & = & 6 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+10}& = & -13 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10+14x } & = & -13 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -13 \color{blue}{-10} \\\Leftrightarrow &19x & = &-23\\\Leftrightarrow & \color{red}{19}x & = &-23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{19} } & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)