Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-12}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12+9x } & = & 11 \color{red}{ -9x }\color{blue}{+12+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & 11 \color{blue}{+12} \\\Leftrightarrow &19x & = &23\\\Leftrightarrow & \color{red}{19}x & = &23\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{23}{19} \\\Leftrightarrow & \color{green}{ x = \frac{23}{19} } & & \\ & V = \left\{ \frac{23}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-8x & = &-11\\\Leftrightarrow & \color{red}{-8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+8}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8-11x } & = & -2 \color{red}{ +11x }\color{blue}{-8-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -2 \color{blue}{-8} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-3}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-x } & = & 14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 14 \color{blue}{+3} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+11}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11-3x } & = & -6 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & -6 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-17\\\Leftrightarrow & \color{red}{-8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+14}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-11x } & = & -3 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -3 \color{blue}{-14} \\\Leftrightarrow &-12x & = &-17\\\Leftrightarrow & \color{red}{-12}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+14}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+14}\color{blue}{-14+13x } & = & -7 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &27x & = &-21\\\Leftrightarrow & \color{red}{27}x & = &-21\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{-21}{27} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-7}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7-7x } & = & -13 \color{red}{ +7x }\color{blue}{+7-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -13 \color{blue}{+7} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+12}& = & -8 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+4x } & = & -8 \color{red}{ -4x }\color{blue}{-12+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &3x & = &-20\\\Leftrightarrow & \color{red}{3}x & = &-20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{3} } & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-5}& = & -6 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-14x } & = & -6 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -6 \color{blue}{+5} \\\Leftrightarrow &-27x & = &-1\\\Leftrightarrow & \color{red}{-27}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-1}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{27} } & & \\ & V = \left\{ \frac{1}{27} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-14}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14-3x } & = & 7 \color{red}{ +3x }\color{blue}{+14-3x } \\\Leftrightarrow & 2x \color{blue}{-3x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-x & = &21\\\Leftrightarrow & \color{red}{-}x & = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-2}& = & 13 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+7x } & = & 13 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 13 \color{blue}{+2} \\\Leftrightarrow &22x & = &15\\\Leftrightarrow & \color{red}{22}x & = &15\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{15}{22} \\\Leftrightarrow & \color{green}{ x = \frac{15}{22} } & & \\ & V = \left\{ \frac{15}{22} \right\} & \\\end{align}\)