Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{-12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & -45x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & -45x+25x& = & 4+12 \\\Leftrightarrow & \color{red}{-20} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-20} & & \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{10}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-20} & = & \color{red}{98x} +49 \\\Leftrightarrow & -84x \color{red}{-20} \color{blue}{+20} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+20} \\\Leftrightarrow & -84x-98x& = & 49+20 \\\Leftrightarrow & \color{red}{-182} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-182} & & \\\Leftrightarrow & x = \frac{-69}{182} & & \\ & V = \left\{ \frac{-69}{182} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{11})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 30x-\frac{24}{11}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{3960}{ \color{blue}{132} }x- \frac{288}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 3960x \color{red}{-288} & = & \color{red}{924x} +55 \\\Leftrightarrow & 3960x \color{red}{-288} \color{blue}{+288} \color{blue}{-924x} & = & \color{red}{924x} +55 \color{blue}{-924x} \color{blue}{+288} \\\Leftrightarrow & 3960x-924x& = & 55+288 \\\Leftrightarrow & \color{red}{3036} x& = & 343 \\\Leftrightarrow & x = \frac{343}{3036} & & \\ & V = \left\{ \frac{343}{3036} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 4x+\frac{4}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-12} \\\Leftrightarrow & 60x+105x& = & 10-12 \\\Leftrightarrow & \color{red}{165} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{165} & & \\ & V = \left\{ \frac{-2}{165} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+18} & = & \color{red}{-168x} +14 \\\Leftrightarrow & -315x \color{red}{+18} \color{blue}{-18} \color{blue}{+168x} & = & \color{red}{-168x} +14 \color{blue}{+168x} \color{blue}{-18} \\\Leftrightarrow & -315x+168x& = & 14-18 \\\Leftrightarrow & \color{red}{-147} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-147} & & \\\Leftrightarrow & x = \frac{4}{147} & & \\ & V = \left\{ \frac{4}{147} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{4})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 21x+\frac{35}{4}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{420}{ \color{blue}{20} }x+ \frac{175}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{-40x} +36 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{+40x} & = & \color{red}{-40x} +36 \color{blue}{+40x} \color{blue}{-175} \\\Leftrightarrow & 420x+40x& = & 36-175 \\\Leftrightarrow & \color{red}{460} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{460} & & \\ & V = \left\{ \frac{-139}{460} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{864}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 864x \color{red}{+135} & = & \color{red}{360x} +80 \\\Leftrightarrow & 864x \color{red}{+135} \color{blue}{-135} \color{blue}{-360x} & = & \color{red}{360x} +80 \color{blue}{-360x} \color{blue}{-135} \\\Leftrightarrow & 864x-360x& = & 80-135 \\\Leftrightarrow & \color{red}{504} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{504} & & \\ & V = \left\{ \frac{-55}{504} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{11})& = & -9x+\frac{9}{5} \\\Leftrightarrow & 28x-\frac{28}{11}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{140}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-140} & = & \color{red}{-495x} +99 \\\Leftrightarrow & 1540x \color{red}{-140} \color{blue}{+140} \color{blue}{+495x} & = & \color{red}{-495x} +99 \color{blue}{+495x} \color{blue}{+140} \\\Leftrightarrow & 1540x+495x& = & 99+140 \\\Leftrightarrow & \color{red}{2035} x& = & 239 \\\Leftrightarrow & x = \frac{239}{2035} & & \\ & V = \left\{ \frac{239}{2035} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{7})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{8}{7}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-88} & = & \color{red}{231x} +42 \\\Leftrightarrow & -1540x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +42 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & -1540x-231x& = & 42+88 \\\Leftrightarrow & \color{red}{-1771} x& = & 130 \\\Leftrightarrow & x = \frac{130}{-1771} & & \\\Leftrightarrow & x = \frac{-130}{1771} & & \\ & V = \left\{ \frac{-130}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{11})& = & -4x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{25}{11}& = & -4x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+25} & = & \color{red}{-44x} +7 \\\Leftrightarrow & -165x \color{red}{+25} \color{blue}{-25} \color{blue}{+44x} & = & \color{red}{-44x} +7 \color{blue}{+44x} \color{blue}{-25} \\\Leftrightarrow & -165x+44x& = & 7-25 \\\Leftrightarrow & \color{red}{-121} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-121} & & \\\Leftrightarrow & x = \frac{18}{121} & & \\ & V = \left\{ \frac{18}{121} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{10}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-30} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -198x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -198x+231x& = & 110+30 \\\Leftrightarrow & \color{red}{33} x& = & 140 \\\Leftrightarrow & x = \frac{140}{33} & & \\ & V = \left\{ \frac{140}{33} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{480}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 480x \color{red}{+48} & = & \color{red}{-140x} +35 \\\Leftrightarrow & 480x \color{red}{+48} \color{blue}{-48} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{-48} \\\Leftrightarrow & 480x+140x& = & 35-48 \\\Leftrightarrow & \color{red}{620} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{620} & & \\ & V = \left\{ \frac{-13}{620} \right\} & \\\end{align}\)