Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-5x-4)& = & 15 \color{red}{+} (2-2x) \\\Leftrightarrow & -15x-12& = &15+2-2x \\\Leftrightarrow & -15x \color{red}{-12} & = &17 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -15x+2x& = &17+12 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-2)& = & -5 \color{red}{-} (9+3x) \\\Leftrightarrow & -8x-8& = &-5-9-3x \\\Leftrightarrow & -8x \color{red}{-8} & = &-14 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -8x+3x& = &-14+8 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x+7)& = & 13 \color{red}{-} (-14+x) \\\Leftrightarrow & 5x+35& = &13+14-x \\\Leftrightarrow & 5x \color{red}{+35} & = &27 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+35} \color{blue}{-35} \color{blue}{+x} & = &27 \color{red}{-x} \color{blue}{+x} \color{blue}{-35} \\\Leftrightarrow & 5x+x& = &27-35 \\\Leftrightarrow & 6x& = &-8 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-8}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-4}{3} & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-5x+7)& = & 1 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x+42& = &1+9-x \\\Leftrightarrow & -30x \color{red}{+42} & = &10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -30x+x& = &10-42 \\\Leftrightarrow & -29x& = &-32 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-32}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{32}{29} & & \\ & V = \left\{ \frac{32}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x-7)& = & -14 \color{red}{-} (1-3x) \\\Leftrightarrow & -10x-14& = &-14-1+3x \\\Leftrightarrow & -10x \color{red}{-14} & = &-15 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -10x-3x& = &-15+14 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (x+7)& = & -10 \color{red}{-} (-3-5x) \\\Leftrightarrow & 3x+21& = &-10+3+5x \\\Leftrightarrow & 3x \color{red}{+21} & = &-7 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 3x-5x& = &-7-21 \\\Leftrightarrow & -2x& = &-28 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-28}{ \color{red}{-2} } \\\Leftrightarrow & x = 14 & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x+7)& = & -14 \color{red}{+} (4+x) \\\Leftrightarrow & -24x+42& = &-14+4+x \\\Leftrightarrow & -24x \color{red}{+42} & = &-10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -24x-x& = &-10-42 \\\Leftrightarrow & -25x& = &-52 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-52}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{52}{25} & & \\ & V = \left\{ \frac{52}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x+3)& = & 13 \color{red}{+} (-4+x) \\\Leftrightarrow & 8x+12& = &13-4+x \\\Leftrightarrow & 8x \color{red}{+12} & = &9 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &9-12 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-7)& = & 10 \color{red}{-} (6+x) \\\Leftrightarrow & -12x-42& = &10-6-x \\\Leftrightarrow & -12x \color{red}{-42} & = &4 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -12x+x& = &4+42 \\\Leftrightarrow & -11x& = &46 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{46}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-46}{11} & & \\ & V = \left\{ \frac{-46}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-3x-3)& = & 3 \color{red}{-} (1+x) \\\Leftrightarrow & -15x-15& = &3-1-x \\\Leftrightarrow & -15x \color{red}{-15} & = &2 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -15x+x& = &2+15 \\\Leftrightarrow & -14x& = &17 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{17}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-17}{14} & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-5)& = & -4 \color{red}{-} (11-5x) \\\Leftrightarrow & -36x-30& = &-4-11+5x \\\Leftrightarrow & -36x \color{red}{-30} & = &-15 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & -36x-5x& = &-15+30 \\\Leftrightarrow & -41x& = &15 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{15}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{-15}{41} & & \\ & V = \left\{ \frac{-15}{41} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x-7)& = & -5 \color{red}{+} (-2-3x) \\\Leftrightarrow & 4x-28& = &-5-2-3x \\\Leftrightarrow & 4x \color{red}{-28} & = &-7 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & 4x+3x& = &-7+28 \\\Leftrightarrow & 7x& = &21 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{21}{ \color{red}{7} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)