Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+14}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14-14x } & = & 4 \color{red}{ +14x }\color{blue}{-14-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-27x & = &-10\\\Leftrightarrow & \color{red}{-27}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-10}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x } & = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+1}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-3x } & = & 3 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & -2x \color{blue}{-3x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-14}& = & 13 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14-7x } & = & 13 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 13 \color{blue}{+14} \\\Leftrightarrow &-10x & = &27\\\Leftrightarrow & \color{red}{-10}x & = &27\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{27}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{10} } & & \\ & V = \left\{ \frac{-27}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+4}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x } & = & 2 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &23x & = &-2\\\Leftrightarrow & \color{red}{23}x & = &-2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+10}& = & -1 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-9x } & = & -1 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -1 \color{blue}{-10} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+7}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7-x } & = & 11 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 11 \color{blue}{-7} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+12}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x } & = & -6 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -6 \color{blue}{-12} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3-x } & = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{-3} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-x } & = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 12 \color{blue}{+14} \\\Leftrightarrow &-5x & = &26\\\Leftrightarrow & \color{red}{-5}x & = &26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{5} } & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{+14}& = & 4 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14+5x } & = & 4 \color{red}{ -5x }\color{blue}{-14+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-4}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-4x } & = & 11 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)