Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-2}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2+5x } & = & 15 \color{red}{ -5x }\color{blue}{+2+5x } \\\Leftrightarrow & 11x \color{blue}{+5x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &16x & = &17\\\Leftrightarrow & \color{red}{16}x & = &17\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{17}{16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{-4}& = & 12 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4+12x } & = & 12 \color{red}{ -12x }\color{blue}{+4+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & 12 \color{blue}{+4} \\\Leftrightarrow &25x & = &16\\\Leftrightarrow & \color{red}{25}x & = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-4}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4-4x } & = & -5 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+9}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-13x } & = & -13 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & -13 \color{blue}{-9} \\\Leftrightarrow &-17x & = &-22\\\Leftrightarrow & \color{red}{-17}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-22}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{22}{17} } & & \\ & V = \left\{ \frac{22}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-4}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-14x } & = & 11 \color{red}{ +14x }\color{blue}{+4-14x } \\\Leftrightarrow & 13x \color{blue}{-14x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+6}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-7x } & = & 7 \color{red}{ +7x }\color{blue}{-6-7x } \\\Leftrightarrow & -3x \color{blue}{-7x } & = & 7 \color{blue}{-6} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+1}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-11x } & = & -6 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -6 \color{blue}{-1} \\\Leftrightarrow &-21x & = &-7\\\Leftrightarrow & \color{red}{-21}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-7}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5-x } & = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{+5} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & 13x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &12x & = &0\\\Leftrightarrow & \color{red}{12}x & = &0\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{0}{12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+7}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+7x } & = & -4 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &22x & = &-11\\\Leftrightarrow & \color{red}{22}x & = &-11\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-11}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-15}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-7x } & = & 4 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-4x & = &19\\\Leftrightarrow & \color{red}{-4}x & = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)