Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+14}& = & -10 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14+13x } & = & -10 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &12x & = &-24\\\Leftrightarrow & \color{red}{12}x & = &-24\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{-24}{12} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-x } & = & -3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -3 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-12\\\Leftrightarrow & \color{red}{-9}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+3}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3+7x } & = & -15 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -15 \color{blue}{-3} \\\Leftrightarrow &19x & = &-18\\\Leftrightarrow & \color{red}{19}x & = &-18\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-18}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{19} } & & \\ & V = \left\{ \frac{-18}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 12x \color{red}{-3}& = & 14 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x } & = & 14 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &23x & = &17\\\Leftrightarrow & \color{red}{23}x & = &17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+14}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-4x } & = & 4 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 3x \color{blue}{-4x } & = & 4 \color{blue}{-14} \\\Leftrightarrow &-x & = &-10\\\Leftrightarrow & \color{red}{-}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x } & = & -14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &-8x & = &-13\\\Leftrightarrow & \color{red}{-8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{8} } & & \\ & V = \left\{ \frac{13}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+5}& = & 4 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+12x } & = & 4 \color{red}{ -12x }\color{blue}{-5+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 4 \color{blue}{-5} \\\Leftrightarrow &17x & = &-1\\\Leftrightarrow & \color{red}{17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-11}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11+7x } & = & 13 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &22x & = &24\\\Leftrightarrow & \color{red}{22}x & = &24\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{24}{22} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{-15}& = & -11 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-8x } & = & -11 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & 9x \color{blue}{-8x } & = & -11 \color{blue}{+15} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-7}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7-10x } & = & -13 \color{red}{ +10x }\color{blue}{+7-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{-6}& = & 9 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6+13x } & = & 9 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 9 \color{blue}{+6} \\\Leftrightarrow &27x & = &15\\\Leftrightarrow & \color{red}{27}x & = &15\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{15}{27} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-5}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-9x } & = & -14 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -14 \color{blue}{+5} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)