Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-x+4)& = & 11 \color{red}{+} (6+x) \\\Leftrightarrow & -6x+24& = &11+6+x \\\Leftrightarrow & -6x \color{red}{+24} & = &17 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -6x-x& = &17-24 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-6)& = & 14 \color{red}{+} (8+x) \\\Leftrightarrow & 36x-36& = &14+8+x \\\Leftrightarrow & 36x \color{red}{-36} & = &22 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 36x-x& = &22+36 \\\Leftrightarrow & 35x& = &58 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{58}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{58}{35} & & \\ & V = \left\{ \frac{58}{35} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (5x+5)& = & -5 \color{red}{+} (7+4x) \\\Leftrightarrow & 15x+15& = &-5+7+4x \\\Leftrightarrow & 15x \color{red}{+15} & = &2 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &2 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 15x-4x& = &2-15 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x-5)& = & 12 \color{red}{-} (10-3x) \\\Leftrightarrow & 4x-10& = &12-10+3x \\\Leftrightarrow & 4x \color{red}{-10} & = &2 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 4x-3x& = &2+10 \\\Leftrightarrow & x& = &12 \\ & V = \left\{ 12 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (5x+7)& = & 5 \color{red}{+} (-12+x) \\\Leftrightarrow & 15x+21& = &5-12+x \\\Leftrightarrow & 15x \color{red}{+21} & = &-7 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 15x-x& = &-7-21 \\\Leftrightarrow & 14x& = &-28 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-28}{ \color{red}{14} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-6)& = & 10 \color{red}{-} (-6+x) \\\Leftrightarrow & -24x-24& = &10+6-x \\\Leftrightarrow & -24x \color{red}{-24} & = &16 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &16 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &16+24 \\\Leftrightarrow & -23x& = &40 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{40}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-40}{23} & & \\ & V = \left\{ \frac{-40}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x+5)& = & -1 \color{red}{-} (-10-2x) \\\Leftrightarrow & -15x+15& = &-1+10+2x \\\Leftrightarrow & -15x \color{red}{+15} & = &9 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & -15x-2x& = &9-15 \\\Leftrightarrow & -17x& = &-6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-1)& = & 4 \color{red}{-} (-8-5x) \\\Leftrightarrow & -6x-2& = &4+8+5x \\\Leftrightarrow & -6x \color{red}{-2} & = &12 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & -6x-5x& = &12+2 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x-3)& = & -7 \color{red}{+} (12+x) \\\Leftrightarrow & -24x-12& = &-7+12+x \\\Leftrightarrow & -24x \color{red}{-12} & = &5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &5+12 \\\Leftrightarrow & -25x& = &17 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{17}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-6x+7)& = & -8 \color{red}{+} (-3+x) \\\Leftrightarrow & -24x+28& = &-8-3+x \\\Leftrightarrow & -24x \color{red}{+28} & = &-11 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &-11-28 \\\Leftrightarrow & -25x& = &-39 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-39}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{39}{25} & & \\ & V = \left\{ \frac{39}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-2)& = & -1 \color{red}{-} (9+x) \\\Leftrightarrow & 8x-4& = &-1-9-x \\\Leftrightarrow & 8x \color{red}{-4} & = &-10 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 8x+x& = &-10+4 \\\Leftrightarrow & 9x& = &-6 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-6}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-2}{3} & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-4x-4)& = & 15 \color{red}{+} (11+3x) \\\Leftrightarrow & -16x-16& = &15+11+3x \\\Leftrightarrow & -16x \color{red}{-16} & = &26 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &26 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -16x-3x& = &26+16 \\\Leftrightarrow & -19x& = &42 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{42}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-42}{19} & & \\ & V = \left\{ \frac{-42}{19} \right\} & \\\end{align}\)