Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+7}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x } & = & 2 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 2 \color{blue}{-7} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-13}& = & -7 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+5x } & = & -7 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &16x & = &6\\\Leftrightarrow & \color{red}{16}x & = &6\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{6}{16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-13}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x } & = & 4 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+13} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{+7}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7-x } & = & -6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-13x & = &-13\\\Leftrightarrow & \color{red}{-13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+1}& = & 5 \color{red}{ +7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1-7x } & = & 5 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 8x \color{blue}{-7x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+13}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13-7x } & = & 10 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -x \color{blue}{-7x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-4x & = &2\\\Leftrightarrow & \color{red}{-4}x & = &2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+9}& = & 15 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+10x } & = & 15 \color{red}{ -10x }\color{blue}{-9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &21x & = &6\\\Leftrightarrow & \color{red}{21}x & = &6\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{6}{21} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x } & = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -11 \color{blue}{+13} \\\Leftrightarrow &-6x & = &2\\\Leftrightarrow & \color{red}{-6}x & = &2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-11}& = & -7 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+5x } & = & -7 \color{red}{ -5x }\color{blue}{+11+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -7 \color{blue}{+11} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & 1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 1 \color{blue}{+5} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)