Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 16x+\frac{12}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{+108} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 1008x \color{red}{+108} \color{blue}{-108} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{-108} \\\Leftrightarrow & 1008x+441x& = & 70-108 \\\Leftrightarrow & \color{red}{1449} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{1449} & & \\ & V = \left\{ \frac{-38}{1449} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{175x} +25 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +25 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -315x-175x& = & 25+84 \\\Leftrightarrow & \color{red}{-490} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-490} & & \\\Leftrightarrow & x = \frac{-109}{490} & & \\ & V = \left\{ \frac{-109}{490} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 20x-\frac{15}{8}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{-15} & = & \color{red}{-56x} +14 \\\Leftrightarrow & 160x \color{red}{-15} \color{blue}{+15} \color{blue}{+56x} & = & \color{red}{-56x} +14 \color{blue}{+56x} \color{blue}{+15} \\\Leftrightarrow & 160x+56x& = & 14+15 \\\Leftrightarrow & \color{red}{216} x& = & 29 \\\Leftrightarrow & x = \frac{29}{216} & & \\ & V = \left\{ \frac{29}{216} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & -4x+\frac{8}{5} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -4x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-75} & = & \color{red}{-220x} +88 \\\Leftrightarrow & 825x \color{red}{-75} \color{blue}{+75} \color{blue}{+220x} & = & \color{red}{-220x} +88 \color{blue}{+220x} \color{blue}{+75} \\\Leftrightarrow & 825x+220x& = & 88+75 \\\Leftrightarrow & \color{red}{1045} x& = & 163 \\\Leftrightarrow & x = \frac{163}{1045} & & \\ & V = \left\{ \frac{163}{1045} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{3})& = & 3x+\frac{3}{2} \\\Leftrightarrow & -14x-\frac{28}{3}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{-56} & = & \color{red}{18x} +9 \\\Leftrightarrow & -84x \color{red}{-56} \color{blue}{+56} \color{blue}{-18x} & = & \color{red}{18x} +9 \color{blue}{-18x} \color{blue}{+56} \\\Leftrightarrow & -84x-18x& = & 9+56 \\\Leftrightarrow & \color{red}{-102} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-102} & & \\\Leftrightarrow & x = \frac{-65}{102} & & \\ & V = \left\{ \frac{-65}{102} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -3x+\frac{3}{7} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{-105x} +15 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{+84} \\\Leftrightarrow & -280x+105x& = & 15+84 \\\Leftrightarrow & \color{red}{-175} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-175} & & \\\Leftrightarrow & x = \frac{-99}{175} & & \\ & V = \left\{ \frac{-99}{175} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 6x-\frac{4}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x- \frac{16}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{-16} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 264x \color{red}{-16} \color{blue}{+16} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{+16} \\\Leftrightarrow & 264x+220x& = & 33+16 \\\Leftrightarrow & \color{red}{484} x& = & 49 \\\Leftrightarrow & x = \frac{49}{484} & & \\ & V = \left\{ \frac{49}{484} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+48} & = & \color{red}{80x} +15 \\\Leftrightarrow & -300x \color{red}{+48} \color{blue}{-48} \color{blue}{-80x} & = & \color{red}{80x} +15 \color{blue}{-80x} \color{blue}{-48} \\\Leftrightarrow & -300x-80x& = & 15-48 \\\Leftrightarrow & \color{red}{-380} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-380} & & \\\Leftrightarrow & x = \frac{33}{380} & & \\ & V = \left\{ \frac{33}{380} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{15}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{660}{ \color{blue}{66} }x+ \frac{90}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 660x \color{red}{+90} & = & \color{red}{-462x} +55 \\\Leftrightarrow & 660x \color{red}{+90} \color{blue}{-90} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{-90} \\\Leftrightarrow & 660x+462x& = & 55-90 \\\Leftrightarrow & \color{red}{1122} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{1122} & & \\ & V = \left\{ \frac{-35}{1122} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{+18} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 198x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & 198x+55x& = & 5-18 \\\Leftrightarrow & \color{red}{253} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{253} & & \\ & V = \left\{ \frac{-13}{253} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{7})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -6x-\frac{12}{7}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-12} & = & \color{red}{49x} +5 \\\Leftrightarrow & -42x \color{red}{-12} \color{blue}{+12} \color{blue}{-49x} & = & \color{red}{49x} +5 \color{blue}{-49x} \color{blue}{+12} \\\Leftrightarrow & -42x-49x& = & 5+12 \\\Leftrightarrow & \color{red}{-91} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-91} & & \\\Leftrightarrow & x = \frac{-17}{91} & & \\ & V = \left\{ \frac{-17}{91} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{9}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-27} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 180x \color{red}{-27} \color{blue}{+27} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+27} \\\Leftrightarrow & 180x+75x& = & 10+27 \\\Leftrightarrow & \color{red}{255} x& = & 37 \\\Leftrightarrow & x = \frac{37}{255} & & \\ & V = \left\{ \frac{37}{255} \right\} & \\\end{align}\)