Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x-1)& = & -12 \color{red}{+} (-8-2x) \\\Leftrightarrow & 9x-3& = &-12-8-2x \\\Leftrightarrow & 9x \color{red}{-3} & = &-20 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 9x+2x& = &-20+3 \\\Leftrightarrow & 11x& = &-17 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-17}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-17}{11} & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (3x-3)& = & -10 \color{red}{+} (5-2x) \\\Leftrightarrow & 15x-15& = &-10+5-2x \\\Leftrightarrow & 15x \color{red}{-15} & = &-5 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 15x+2x& = &-5+15 \\\Leftrightarrow & 17x& = &10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-6)& = & 9 \color{red}{+} (-14-3x) \\\Leftrightarrow & 4x-12& = &9-14-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-5 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-5 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &-5+12 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x-6)& = & -15 \color{red}{-} (7+x) \\\Leftrightarrow & -6x-12& = &-15-7-x \\\Leftrightarrow & -6x \color{red}{-12} & = &-22 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &-22+12 \\\Leftrightarrow & -5x& = &-10 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-10}{ \color{red}{-5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-2x+2)& = & -5 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x+6& = &-5-2+5x \\\Leftrightarrow & -6x \color{red}{+6} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -6x-5x& = &-7-6 \\\Leftrightarrow & -11x& = &-13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{13}{11} & & \\ & V = \left\{ \frac{13}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (6x+7)& = & -15 \color{red}{-} (12+x) \\\Leftrightarrow & 36x+42& = &-15-12-x \\\Leftrightarrow & 36x \color{red}{+42} & = &-27 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-27 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 36x+x& = &-27-42 \\\Leftrightarrow & 37x& = &-69 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-69}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-69}{37} & & \\ & V = \left\{ \frac{-69}{37} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-2)& = & -11 \color{red}{-} (10+x) \\\Leftrightarrow & -20x-10& = &-11-10-x \\\Leftrightarrow & -20x \color{red}{-10} & = &-21 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &-21+10 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-3x-5)& = & 9 \color{red}{-} (-14+2x) \\\Leftrightarrow & -15x-25& = &9+14-2x \\\Leftrightarrow & -15x \color{red}{-25} & = &23 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+2x} & = &23 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+25} \\\Leftrightarrow & -15x+2x& = &23+25 \\\Leftrightarrow & -13x& = &48 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{48}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-48}{13} & & \\ & V = \left\{ \frac{-48}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-5x+6)& = & -7 \color{red}{+} (4+4x) \\\Leftrightarrow & -25x+30& = &-7+4+4x \\\Leftrightarrow & -25x \color{red}{+30} & = &-3 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &-3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & -25x-4x& = &-3-30 \\\Leftrightarrow & -29x& = &-33 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-33}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{33}{29} & & \\ & V = \left\{ \frac{33}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+4)& = & 9 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x+16& = &9+6-x \\\Leftrightarrow & -24x \color{red}{+16} & = &15 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -24x+x& = &15-16 \\\Leftrightarrow & -23x& = &-1 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-1}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x-6)& = & -9 \color{red}{+} (12+x) \\\Leftrightarrow & -12x-18& = &-9+12+x \\\Leftrightarrow & -12x \color{red}{-18} & = &3 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &3+18 \\\Leftrightarrow & -13x& = &21 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{21}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-1)& = & 11 \color{red}{-} (1-2x) \\\Leftrightarrow & 5x-5& = &11-1+2x \\\Leftrightarrow & 5x \color{red}{-5} & = &10 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 5x-2x& = &10+5 \\\Leftrightarrow & 3x& = &15 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{15}{ \color{red}{3} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)