Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-4}& = & 14 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4+7x } & = & 14 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & 14 \color{blue}{+4} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-11}& = & 3 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-5x } & = & 3 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & -14x \color{blue}{-5x } & = & 3 \color{blue}{+11} \\\Leftrightarrow &-19x & = &14\\\Leftrightarrow & \color{red}{-19}x & = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-12}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12-10x } & = & 10 \color{red}{ +10x }\color{blue}{+12-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &3x & = &22\\\Leftrightarrow & \color{red}{3}x & = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-11}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11-7x } & = & 7 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &-4x & = &18\\\Leftrightarrow & \color{red}{-4}x & = &18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+15}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-x } & = & -11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-26\\\Leftrightarrow & \color{red}{-7}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-26}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+5}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5-13x } & = & 11 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -x \color{blue}{-13x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+10}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-13x } & = & -6 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -6 \color{blue}{-10} \\\Leftrightarrow &-25x & = &-16\\\Leftrightarrow & \color{red}{-25}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-16}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-7}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-4x } & = & 8 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 8 \color{blue}{+7} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-x } & = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 13 \color{blue}{+6} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+6}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-6x } & = & -6 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -6 \color{blue}{-6} \\\Leftrightarrow &-5x & = &-12\\\Leftrightarrow & \color{red}{-5}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+3}& = & 12 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+9x } & = & 12 \color{red}{ -9x }\color{blue}{-3+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 12 \color{blue}{-3} \\\Leftrightarrow &19x & = &9\\\Leftrightarrow & \color{red}{19}x & = &9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-12}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & -13 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -13 \color{blue}{+12} \\\Leftrightarrow &-4x & = &-1\\\Leftrightarrow & \color{red}{-4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)