Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+2}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-x } & = & 8 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 8 \color{blue}{-2} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-9}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9-12x } & = & 6 \color{red}{ +12x }\color{blue}{+9-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{-9}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-9}\color{blue}{+9-10x } & = & -6 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-7x & = &3\\\Leftrightarrow & \color{red}{-7}x & = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-7}& = & 12 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+6x } & = & 12 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &19x & = &19\\\Leftrightarrow & \color{red}{19}x & = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-x } & = & 8 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &10x & = &15\\\Leftrightarrow & \color{red}{10}x & = &15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-15}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+13x } & = & 8 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &20x & = &23\\\Leftrightarrow & \color{red}{20}x & = &23\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{23}{20} \\\Leftrightarrow & \color{green}{ x = \frac{23}{20} } & & \\ & V = \left\{ \frac{23}{20} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{-7}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-7}\color{blue}{+7-x } & = & -3 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-14x & = &4\\\Leftrightarrow & \color{red}{-14}x & = &4\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{4}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-6}& = & 7 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+13x } & = & 7 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &23x & = &13\\\Leftrightarrow & \color{red}{23}x & = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & 3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 3 \color{blue}{-2} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-6}& = & -7 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+12x } & = & -7 \color{red}{ -12x }\color{blue}{+6+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & -7 \color{blue}{+6} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+1}& = & 6 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-10x } & = & 6 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 6 \color{blue}{-1} \\\Leftrightarrow &3x & = &5\\\Leftrightarrow & \color{red}{3}x & = &5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)