Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3-x } & = & 3 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+13}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-9x } & = & 8 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x } & = & 8 \color{blue}{-13} \\\Leftrightarrow &-20x & = &-5\\\Leftrightarrow & \color{red}{-20}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-13}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-7x } & = & -8 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & -8 \color{blue}{+13} \\\Leftrightarrow &-20x & = &5\\\Leftrightarrow & \color{red}{-20}x & = &5\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{5}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-8}& = & 15 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8+9x } & = & 15 \color{red}{ -9x }\color{blue}{+8+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 15 \color{blue}{+8} \\\Leftrightarrow &23x & = &23\\\Leftrightarrow & \color{red}{23}x & = &23\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{23}{23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-7}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-5x } & = & -8 \color{red}{ +5x }\color{blue}{+7-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-15}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-15}\color{blue}{+15+9x } & = & -2 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -2 \color{blue}{+15} \\\Leftrightarrow &14x & = &13\\\Leftrightarrow & \color{red}{14}x & = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+8}& = & -1 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-10x } & = & -1 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-19x & = &-9\\\Leftrightarrow & \color{red}{-19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+1}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-x } & = & 5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 5 \color{blue}{-1} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-10}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x } & = & 15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &-15x & = &25\\\Leftrightarrow & \color{red}{-15}x & = &25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-4}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-4}\color{blue}{+4-3x } & = & -2 \color{red}{ +3x }\color{blue}{+4-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+4}& = & -2 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4-4x } & = & -2 \color{red}{ +4x }\color{blue}{-4-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -2 \color{blue}{-4} \\\Leftrightarrow &5x & = &-6\\\Leftrightarrow & \color{red}{5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{+2}& = & -10 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2+14x } & = & -10 \color{red}{ -14x }\color{blue}{-2+14x } \\\Leftrightarrow & 5x \color{blue}{+14x } & = & -10 \color{blue}{-2} \\\Leftrightarrow &19x & = &-12\\\Leftrightarrow & \color{red}{19}x & = &-12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\ & V = \left\{ \frac{-12}{19} \right\} & \\\end{align}\)