Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x+5)& = & -6 \color{red}{+} (-14+x) \\\Leftrightarrow & -30x+30& = &-6-14+x \\\Leftrightarrow & -30x \color{red}{+30} & = &-20 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &-20-30 \\\Leftrightarrow & -31x& = &-50 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-50}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{50}{31} & & \\ & V = \left\{ \frac{50}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x-7)& = & 1 \color{red}{+} (-3+3x) \\\Leftrightarrow & -16x-28& = &1-3+3x \\\Leftrightarrow & -16x \color{red}{-28} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -16x-3x& = &-2+28 \\\Leftrightarrow & -19x& = &26 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{26}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-26}{19} & & \\ & V = \left\{ \frac{-26}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+7)& = & -8 \color{red}{-} (2-3x) \\\Leftrightarrow & -10x+14& = &-8-2+3x \\\Leftrightarrow & -10x \color{red}{+14} & = &-10 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -10x-3x& = &-10-14 \\\Leftrightarrow & -13x& = &-24 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-24}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (6x-7)& = & 4 \color{red}{-} (10+x) \\\Leftrightarrow & 12x-14& = &4-10-x \\\Leftrightarrow & 12x \color{red}{-14} & = &-6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &-6+14 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x-4)& = & -13 \color{red}{-} (4+x) \\\Leftrightarrow & 6x-24& = &-13-4-x \\\Leftrightarrow & 6x \color{red}{-24} & = &-17 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 6x+x& = &-17+24 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x-7)& = & 4 \color{red}{-} (14-3x) \\\Leftrightarrow & 10x-14& = &4-14+3x \\\Leftrightarrow & 10x \color{red}{-14} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & 10x-3x& = &-10+14 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x-4)& = & 15 \color{red}{-} (2+x) \\\Leftrightarrow & 24x-16& = &15-2-x \\\Leftrightarrow & 24x \color{red}{-16} & = &13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & 24x+x& = &13+16 \\\Leftrightarrow & 25x& = &29 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{29}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{29}{25} & & \\ & V = \left\{ \frac{29}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-4)& = & -7 \color{red}{-} (-14+3x) \\\Leftrightarrow & -20x-16& = &-7+14-3x \\\Leftrightarrow & -20x \color{red}{-16} & = &7 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-16} \color{blue}{+16} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+16} \\\Leftrightarrow & -20x+3x& = &7+16 \\\Leftrightarrow & -17x& = &23 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{23}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-23}{17} & & \\ & V = \left\{ \frac{-23}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+6)& = & 13 \color{red}{-} (7+x) \\\Leftrightarrow & 6x+18& = &13-7-x \\\Leftrightarrow & 6x \color{red}{+18} & = &6 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &6-18 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-4)& = & -7 \color{red}{-} (-13+x) \\\Leftrightarrow & -8x-8& = &-7+13-x \\\Leftrightarrow & -8x \color{red}{-8} & = &6 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -8x+x& = &6+8 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x-1)& = & -12 \color{red}{+} (10+x) \\\Leftrightarrow & 36x-6& = &-12+10+x \\\Leftrightarrow & 36x \color{red}{-6} & = &-2 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 36x-x& = &-2+6 \\\Leftrightarrow & 35x& = &4 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{4}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{4}{35} & & \\ & V = \left\{ \frac{4}{35} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x+2)& = & -14 \color{red}{-} (8+x) \\\Leftrightarrow & 12x+12& = &-14-8-x \\\Leftrightarrow & 12x \color{red}{+12} & = &-22 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 12x+x& = &-22-12 \\\Leftrightarrow & 13x& = &-34 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-34}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-34}{13} & & \\ & V = \left\{ \frac{-34}{13} \right\} & \\\end{align}\)