Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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