Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 350x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & 350x+245x& = & 42+30 \\\Leftrightarrow & \color{red}{595} x& = & 72 \\\Leftrightarrow & x = \frac{72}{595} & & \\ & V = \left\{ \frac{72}{595} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{9})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 8x-\frac{10}{9}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-70} & = & \color{red}{-441x} +45 \\\Leftrightarrow & 504x \color{red}{-70} \color{blue}{+70} \color{blue}{+441x} & = & \color{red}{-441x} +45 \color{blue}{+441x} \color{blue}{+70} \\\Leftrightarrow & 504x+441x& = & 45+70 \\\Leftrightarrow & \color{red}{945} x& = & 115 \\\Leftrightarrow & x = \frac{115}{945} & & \\\Leftrightarrow & x = \frac{23}{189} & & \\ & V = \left\{ \frac{23}{189} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-88} & = & \color{red}{-693x} +90 \\\Leftrightarrow & -594x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +90 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -594x+693x& = & 90+88 \\\Leftrightarrow & \color{red}{99} x& = & 178 \\\Leftrightarrow & x = \frac{178}{99} & & \\ & V = \left\{ \frac{178}{99} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+330} & = & \color{red}{385x} +49 \\\Leftrightarrow & 924x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +49 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & 924x-385x& = & 49-330 \\\Leftrightarrow & \color{red}{539} x& = & -281 \\\Leftrightarrow & x = \frac{-281}{539} & & \\ & V = \left\{ \frac{-281}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -8x+\frac{6}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+30} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -440x \color{red}{+30} \color{blue}{-30} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{-30} \\\Leftrightarrow & -440x+495x& = & 22-30 \\\Leftrightarrow & \color{red}{55} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{55} & & \\ & V = \left\{ \frac{-8}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{3})& = & 4x+\frac{4}{7} \\\Leftrightarrow & -15x-\frac{10}{3}& = & 4x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-70} & = & \color{red}{84x} +12 \\\Leftrightarrow & -315x \color{red}{-70} \color{blue}{+70} \color{blue}{-84x} & = & \color{red}{84x} +12 \color{blue}{-84x} \color{blue}{+70} \\\Leftrightarrow & -315x-84x& = & 12+70 \\\Leftrightarrow & \color{red}{-399} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-399} & & \\\Leftrightarrow & x = \frac{-82}{399} & & \\ & V = \left\{ \frac{-82}{399} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{1}{2})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{7}{2}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+21} & = & \color{red}{54x} +20 \\\Leftrightarrow & 168x \color{red}{+21} \color{blue}{-21} \color{blue}{-54x} & = & \color{red}{54x} +20 \color{blue}{-54x} \color{blue}{-21} \\\Leftrightarrow & 168x-54x& = & 20-21 \\\Leftrightarrow & \color{red}{114} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{114} & & \\ & V = \left\{ \frac{-1}{114} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 30x+\frac{12}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x+ \frac{24}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{+24} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 420x \color{red}{+24} \color{blue}{-24} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{-24} \\\Leftrightarrow & 420x+98x& = & 49-24 \\\Leftrightarrow & \color{red}{518} x& = & 25 \\\Leftrightarrow & x = \frac{25}{518} & & \\ & V = \left\{ \frac{25}{518} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -80x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{-115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-115} & & \\\Leftrightarrow & x = \frac{-18}{115} & & \\ & V = \left\{ \frac{-18}{115} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{-60} & = & \color{red}{70x} +35 \\\Leftrightarrow & 252x \color{red}{-60} \color{blue}{+60} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+60} \\\Leftrightarrow & 252x-70x& = & 35+60 \\\Leftrightarrow & \color{red}{182} x& = & 95 \\\Leftrightarrow & x = \frac{95}{182} & & \\ & V = \left\{ \frac{95}{182} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{35}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-35} & = & \color{red}{-9x} +8 \\\Leftrightarrow & -105x \color{red}{-35} \color{blue}{+35} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{+35} \\\Leftrightarrow & -105x+9x& = & 8+35 \\\Leftrightarrow & \color{red}{-96} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-96} & & \\\Leftrightarrow & x = \frac{-43}{96} & & \\ & V = \left\{ \frac{-43}{96} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{225x} +10 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & -540x-225x& = & 10-108 \\\Leftrightarrow & \color{red}{-765} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-765} & & \\\Leftrightarrow & x = \frac{98}{765} & & \\ & V = \left\{ \frac{98}{765} \right\} & \\\end{align}\)