Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(13x+7=12+14x\)
2. \(-10x+7=-8+11x\)
3. \(-14x+1=10+x\)
4. \(6x-4=-9+x\)
5. \(-13x-8=8+14x\)
6. \(8x-14=5-13x\)
7. \(x+11=13+0x\)
8. \(6x+2=13+x\)
9. \(-10x+8=10+x\)
10. \(-11x-10=5+6x\)
11. \(7x-6=-8+11x\)
12. \(-8x+2=4+9x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+7}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-14x } & = & 12 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 12 \color{blue}{-7} \\\Leftrightarrow &-x & = &5\\\Leftrightarrow & \color{red}{-}x & = &5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{5}{-1} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+7}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-11x } & = & -8 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -8 \color{blue}{-7} \\\Leftrightarrow &-21x & = &-15\\\Leftrightarrow & \color{red}{-21}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-15}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+1}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x } & = & 10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-1} \\\Leftrightarrow &-15x & = &9\\\Leftrightarrow & \color{red}{-15}x & = &9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-x } & = & -9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & -9 \color{blue}{+4} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{-8}& = & 8 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-14x } & = & 8 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &-27x & = &16\\\Leftrightarrow & \color{red}{-27}x & = &16\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{16}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{27} } & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-14}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14+13x } & = & 5 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & 8x \color{blue}{+13x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &21x & = &19\\\Leftrightarrow & \color{red}{21}x & = &19\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}} & = & \frac{19}{21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+11}& = & 13 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+0x } & = & 13 \color{red}{ +0x }\color{blue}{-11+0x } \\\Leftrightarrow & x \color{blue}{+0x } & = & 13 \color{blue}{-11} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{+2}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x } & = & 13 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &5x & = &11\\\Leftrightarrow & \color{red}{5}x & = &11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{+8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x } & = & 10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-8} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-10}& = & 5 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-6x } & = & 5 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 5 \color{blue}{+10} \\\Leftrightarrow &-17x & = &15\\\Leftrightarrow & \color{red}{-17}x & = &15\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{15}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{17} } & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-6}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6-11x } & = & -8 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+2}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-9x } & = & 4 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -8x \color{blue}{-9x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-17x & = &2\\\Leftrightarrow & \color{red}{-17}x & = &2\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{2}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)